venn diagram with problem solving

Venn Diagram Examples, Problems and Solutions

On this page:

• What is Venn diagram? Definition and meaning.
• Venn diagram formula with an explanation.
• Examples of 2 and 3 sets Venn diagrams: practice problems with solutions, questions, and answers.
• Simple 4 circles Venn diagram with word problems.
• Compare and contrast Venn diagram example.

Let’s define it:

A Venn Diagram is an illustration that shows logical relationships between two or more sets (grouping items). Venn diagram uses circles (both overlapping and nonoverlapping) or other shapes.

Commonly, Venn diagrams show how given items are similar and different.

Despite Venn diagram with 2 or 3 circles are the most common type, there are also many diagrams with a larger number of circles (5,6,7,8,10…). Theoretically, they can have unlimited circles.

Venn Diagram General Formula

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

Don’t worry, there is no need to remember this formula, once you grasp the meaning. Let’s see the explanation with an example.

This is a very simple Venn diagram example that shows the relationship between two overlapping sets X, Y.

X – the number of items that belong to set A Y – the number of items that belong to set B Z – the number of items that belong to set A and B both

From the above Venn diagram, it is quite clear that

n(A) = x + z n(B) = y + z n(A ∩ B) = z n(A ∪ B) = x +y+ z.

Now, let’s move forward and think about Venn Diagrams with 3 circles.

Following the same logic, we can write the formula for 3 circles Venn diagram :

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(C ∩ A) + n(A ∩ B ∩ C)

Venn Diagram Examples (Problems with Solutions)

As we already know how the Venn diagram works, we are going to give some practical examples (problems with solutions) from the real life.

2 Circle Venn Diagram Examples (word problems):

Suppose that in a town, 800 people are selected by random types of sampling methods . 280 go to work by car only, 220 go to work by bicycle only and 140 use both ways – sometimes go with a car and sometimes with a bicycle.

Here are some important questions we will find the answers:

• How many people go to work by car only?
• How many people go to work by bicycle only?
• How many people go by neither car nor bicycle?
• How many people use at least one of both transportation types?
• How many people use only one of car or bicycle?

The following Venn diagram represents the data above:

Now, we are going to answer our questions:

• Number of people who go to work by car only = 280
• Number of people who go to work by bicycle only = 220
• Number of people who go by neither car nor bicycle = 160
• Number of people who use at least one of both transportation types = n(only car) + n(only bicycle) + n(both car and bicycle) = 280 + 220 + 140 = 640
• Number of people who use only one of car or bicycle = 280 + 220 = 500

Note: The number of people who go by neither car nor bicycle (160) is illustrated outside of the circles. It is a common practice the number of items that belong to none of the studied sets, to be illustrated outside of the diagram circles.

We will deep further with a more complicated triple Venn diagram example.

3 Circle Venn Diagram Examples:

For the purposes of a marketing research , a survey of 1000 women is conducted in a town. The results show that 52 % liked watching comedies, 45% liked watching fantasy movies and 60% liked watching romantic movies. In addition, 25% liked watching comedy and fantasy both, 28% liked watching romantic and fantasy both and 30% liked watching comedy and romantic movies both. 6% liked watching none of these movie genres.

Here are our questions we should find the answer:

• How many women like watching all the three movie genres?
• Find the number of women who like watching only one of the three genres.
• Find the number of women who like watching at least two of the given genres.

Let’s represent the data above in a more digestible way using the Venn diagram formula elements:

• n(C) = percentage of women who like watching comedy = 52%
• n(F ) = percentage of women who like watching fantasy = 45%
• n(R) = percentage of women who like watching romantic movies= 60%
• n(C∩F) = 25%; n(F∩R) = 28%; n(C∩R) = 30%
• Since 6% like watching none of the given genres so, n (C ∪ F ∪ R) = 94%.

Now, we are going to apply the Venn diagram formula for 3 circles. 

94% = 52% + 45% + 60% – 25% – 28% – 30% + n (C ∩ F ∩ R)

Solving this simple math equation, lead us to:

n (C ∩ F ∩ R)  = 20%

It is a great time to make our Venn diagram related to the above situation (problem):

See, the Venn diagram makes our situation much more clear!

From the Venn diagram example, we can answer our questions with ease.

• The number of women who like watching all the three genres = 20% of 1000 = 200.
• Number of women who like watching only one of the three genres = (17% + 12% + 22%) of 1000 = 510
• The number of women who like watching at least two of the given genres = (number of women who like watching only two of the genres) +(number of women who like watching all the three genres) = (10 + 5 + 8 + 20)% i.e. 43% of 1000 = 430.

As we mentioned above 2 and 3 circle diagrams are much more common for problem-solving in many areas such as business, statistics, data science and etc. However, 4 circle Venn diagram also has its place.

4 Circles Venn Diagram Example:

A set of students were asked to tell which sports they played in school.

The options are: Football, Hockey, Basketball, and Netball.

Here is the list of the results:

The next step is to draw a Venn diagram to show the data sets we have.

It is very clear who plays which sports. As you see the diagram also include the student who does not play any sports (Dorothy) by putting her name outside of the 4 circles.

From the above Venn diagram examples, it is obvious that this graphical tool can help you a lot in representing a variety of data sets. Venn diagram also is among the most popular types of graphs for identifying similarities and differences .

Compare and Contrast Venn Diagram Example:

The following compare and contrast example of Venn diagram compares the features of birds and bats:

Tools for creating Venn diagrams

It is quite easy to create Venn diagrams, especially when you have the right tool. Nowadays, one of the most popular way to create them is with the help of paid or free graphing software tools such as:

You can use Microsoft products such as:

Some free mind mapping tools are also a good solution. Finally, you can simply use a sheet of paper or a whiteboard.

Conclusion:

A Venn diagram is a simple but powerful way to represent the relationships between datasets. It makes understanding math, different types of data analysis , set theory and business information easier and more fun for you.

Besides of using Venn diagram examples for problem-solving and comparing, you can use them to present passion, talent, feelings, funny moments and etc.

Be it data science or real-world situations, Venn diagrams are a great weapon in your hand to deal with almost any kind of information.

If you need more chart examples, our posts fishbone diagram examples and what does scatter plot show might be of help.

About The Author

Silvia Valcheva

Silvia Valcheva is a digital marketer with over a decade of experience creating content for the tech industry. She has a strong passion for writing about emerging software and technologies such as big data, AI (Artificial Intelligence), IoT (Internet of Things), process automation, etc.

Well explained I hope more on this one

WELL STRUCTURED CONTENT AND ENLIGHTNING AS WELL

Leave a Reply Cancel Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed .

Venn Diagram Calculator

More options are available after generating the Venn Diagram, including the ability to change the opacity of the filling and the colors of the borders.

Venn diagram online

Venn diagram example, how to use the venn diagram calculator:, 1. data list:.

• In this case, the " Output " field will appear, and you can choose one of the following options:

2. Number of data items:

• For groups with intersections, you can enter two numbers:

How to solve a Venn diagram problem.

When problem contains numbers of items, when problem contains data lists, calculators.

Venn Diagram Questions

Venn diagram questions with solutions are given here for students to practice various questions based on Venn diagrams. These questions are beneficial for both school examinations and competitive exams. Practising these questions will develop a skill to solve any problem on Venn diagrams quickly.

Venn diagrams were first introduced by John Venn to represent various propositions in a diagrammatic way. Venn diagrams are used for representing relationships between given sets. For example, natural numbers and whole numbers are subsets of integers represented by the Venn diagram:

Using Venn diagrams, we can easily understand whether given sets are subsets of each other or disjoint sets or have something in common.

• Intersection of Sets
• Union of Sets
• Complement of Set
• Set Operations

Following are some set operations and their meaning useful while solving problems on the Venn diagram:

Some important formulae:

Venn Diagram Questions with Solution

Let us practice some questions based on Venn diagrams.

Question 1: If A and B are two sets such that number of elements in A is 24, number of elements in B is 22 and number of elements in both A and B is 8, find:

(i) n(A ∪ B)

(ii) n(A – B)

(ii) n(B – A)

Given, n(A) = 24, n(B) = 22 and n(A ∩ B) = 8

The Venn diagram for the given information is:

(i) n(A ∪ B) = n(A) + n(B) – n(A ∩ B) = 24 + 22 – 8 = 38.

(ii) n(A – B) = n(A) – n(A ∩ B) = 24 – 8 = 16.

(iii) n(B – A) = n(B) – n(A ∩ B) = 22 – 8 = 14.

Question 2: According to the survey made among 200 students, 140 students like cold drinks, 120 students like milkshakes and 80 like both. How many students like atleast one of the drinks?

Number of students like cold drinks = n(A) = 140

Number of students like milkshake = n(B) = 120

Number of students like both = n(A ∩ B) = 80

Number of students like atleast one of the drinks = n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

= 140 + 120 – 80

Question 3: In a group of 500 people, 350 people can speak English, and 400 people can speak Hindi. Find how many people can speak both languages?

Let H be the set of people who can speak Hindi and E be the set of people who can speak English. Then,

n(H ∪ E) = 500

We have to find n(H ∩ E).

Now, n(H ∪ E) = n(H) + n(E) – n(H ∩ E)

⇒ 500 = 400 + 350 – n(H ∩ E)

⇒ n(H ∩ E) = 750 – 500 = 250.

∴ 250 people can speak both languages.

Questions 4: The following Venn diagram shows games played by the number of students in a class:

How many students like only cricket and only football?

As per the given Venn diagram,

Number of students only like cricket = 7

Number of students only like football = 14

∴ Number of students like only cricket and only football = 7 + 14 = 21.

Question 5: In a class of 40 students, 20 have chosen Mathematics, 15 have chosen mathematics but not biology. If every student has chosen either mathematics or biology or both, find the number of students who chose both mathematics and biology and the number of students chose biology but not mathematics.

Let, M ≡ Set of students who chose mathematics

B ≡ Set of students who chose biology

n(M ∪ B) = 40

n(B) = n(M ∪ B) – n(M)

⇒ n(B) = 40 – 20 = 20

n(M – B) = 15

n(M) = n(M – B) + n(M ∩ B)

⇒ 20 = 15 + n(M ∩ B)

⇒ n(M ∩ B) = 20 – 15 = 5

n(B – M) = n(B) – n(M ∩ B)

⇒ n(B – M) = 20 – 5 = 15

Question 6: Represent The following as Venn diagram:

(i) A’ ∩ (B ∪ C)

(ii) A’ ∩ (C – B)

Question 7: In a survey among 140 students, 60 likes to play videogames, 70 likes to play indoor games, 75 likes to play outdoor games, 30 play indoor and outdoor games, 18 like to play video games and outdoor games, 42 play video games and indoor games and 8 likes to play all types of games. Use the Venn diagram to find

(i) students who play only outdoor games

(ii) students who play video games and indoor games, but not outdoor games.

Let V ≡ Play video games

I ≡ Play indoor games

O ≡ Play outdoor games

n(V) = 60, n(I) = 70, n(O) = 75

n(I ∩ O) = 30, n(V ∩ O) = 18, n(V ∩ I) = 42

n(V ∩ I ∩ O) = 8

Hence, by Venn diagram

Number of students only like to play only outdoor games = 35

Number of students like to play video games and indoor games but not outdoor games = 34

Note : Always begin to fill the Venn diagram from the innermost part.

Question 8: Using the Venn diagrams, verify (P ∩ Q) ∪ R = (P ∪ R) ∩ (Q ∪ R).

The shaded portion represents (P ∩ Q) ∪ R in the Venn diagram.

Comparing both the shaded portion in both the Venn diagram, we get (P ∩ Q) ∪ R = (P ∪ R) ∩ (Q ∪ R).

Question 9: Prove using the Venn diagram: (B – A) ∪ (A ∩ B) = B.

From the Venn diagram, it is clear that (B – A) ∪ (A ∩ B) = B

Question 10: In a survey, it is found that 21 people read English newspaper, 26 people read Hindi newspaper, and 29 people read regional language newspaper. If 14 people read both English and Hindi newspapers; 15 people read both Hindi and regional language newspapers; 12 people read both English and regional language newspaper and 8 read all types of newspapers, find:

(i) How many people were surveyed?

(ii) How many people read only regional language newspapers?

Let A ≡ People who read English newspapers.

B ≡ People who read Hindi newspapers.

C ≡ People who read Hindi newspapers.

n(A) = 21, n(B) = 26, n(C) = 29

n(A ∩ B) = 14, n(B ∩ C) = 15, n(A ∩ C) = 12

n(A ∩ B ∩ C) = 8

(i) Number of people surveyed = n(A ∪ B ∪ C) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A ∩ B ∩ C) = 21 + 26 + 29 – 14 – 15 – 12 + 8 = 43

(ii) By the Venn diagram, number of people who only read regional language newspapers = 10.

Video Lesson on Introduction to Sets

Practice Questions on Venn Diagrams

1. Verify using the Venn diagram:

(i) A – B = A ∩ B C

(ii) (A ∩ B) C = A C ∪ B C

2. For given two sets P and Q, n(P – Q) = 24, n(Q – P) = 19 and n(P ∩ Q) = 11, find:

(iii) n (P ∪ Q)

3. In a group of 65 people, 40 like tea and 10 like both tea and coffee. Find

(i) how many like coffee only and not tea?

(ii) how many like coffee?

4. In a sports tournament, 38 medals were awarded for 500 m sprint, 15 medals were awarded for Javelin throw, and 20 medals were awarded for a long jump. If these medals were awarded to 58 participants and among them only three medals in all three sports, how many received exactly two medals?

Keep visiting BYJU’S to get more such Maths lessons in a simple, concise and easy to understand way. Also, register at BYJU’S – The Learning App to get complete assistance for Maths preparation with video lessons, notes, tips and other study materials.

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

• Announcements
• Brainstorming
• Development
• HR Planning
• Infographics
• IT & Operations
• Marketing & Sales
• Meeting & Visual Collaboration
• Product Management
• Production & Manufacturing
• Project Management
• Remote Working
• Research & Analysis
• Software Teams
• Strategy & Planning
• Template Roundup
• Uncategorized

Venn Diagram Examples for Problem Solving

Updated on: 13 September 2022

What is a Venn Diagram?

Venn diagrams define all the possible relationships between collections of sets. The most basic Venn diagrams simply consist of multiple circular boundaries describing the range of sets.

The overlapping areas between the two boundaries describe the elements which are common between the two, while the areas that aren’t overlapping house the elements that are different. Venn diagrams are used often in math that people tend to assume they are used only to solve math problems. But as the 3 circle Venn diagram below shows it can be used to solve many other problems.

Though the above diagram may look complicated, it is actually very easy to understand. Although Venn diagrams can look complex when solving business processes understanding of the meaning of the boundaries and what they stand for can simplify the process to a great extent. Let us have a look at a few examples which demonstrate how Venn diagrams can make problem solving much easier.

Example 1: Company’s Hiring Process

The first Venn diagram example demonstrates a company’s employee shortlisting process. The Human Resources department looks for several factors when short-listing candidates for a position, such as experience, professional skills and leadership competence. Now, all of these qualities are different from each other, and may or may not be present in some candidates. However, the best candidates would be those that would have all of these qualities combined.

The candidate who has all three qualities is the perfect match for your organization. So by using simple Venn Diagrams like the one above, a company can easily demonstrate its hiring processes and make the selection process much easier.

A colorful and precise Venn diagram like the above can be easily created using our Venn diagram software and we have professionally designed Venn diagram templates for you to get started fast too.

Example 2: Investing in a Location

The second Venn diagram example takes things a step further and takes a look at how a company can use a Venn diagram to decide a suitable office location. The decision will be based on economic, social and environmental factors.

In a perfect scenario you’ll find a location that has all the above factors in equal measure. But if you fail to find such a location then you can decide which factor is most important to you. Whatever the priority because you already have listed down the locations making the decision becomes easier.

Example 3: Choosing a Dream Job

The last example will reflect on how one of the life’s most complicated questions can be easily answered using a Venn diagram. Choosing a dream job is something that has stumped most college graduates, but with a single Venn diagram, this thought process can be simplified to a great extent.

First, single out the factors which matter in choosing a dream job, such as things that you love to do, things you’re good at, and finally, earning potential. Though most of us dream of being a celebrity and coming on TV, not everyone is gifted with acting skills, and that career path may not be the most viable. Instead, choosing something that you are good at, that you love to do along with something that has a good earning potential would be the most practical choice.

A job which includes all of these three criteria would, therefore, be the dream job for someone. The three criteria need not necessarily be the same, and can be changed according to the individual’s requirements.

So you see, even the most complicated processes can be simplified by using these simple Venn diagrams.

Join over thousands of organizations that use Creately to brainstorm, plan, analyze, and execute their projects successfully.

More Related Articles

Great article, and all true, but.. I hate venn diagrams! I don’t know why, they’ve just never seemed to work for me. Frustrating!

Hey thanks for writing. It helped me in many ways Thanks again 🙂

Hi Nishadha,

Nice article! I love Venn Diagrams because nothing comes to close to expressing the logical relationships between different sets of elements that well. With Microsoft Word 2003 you can create fantastic looking and colorful Venn Diagrams on the fly, with as many elements and colors as you need.

Hi Worli, Yes, Venn diagrams are a good way to solve problems, it’s a shame that it’s sort of restricted to the mathematics subject. MS Word do provides some nice options to create Venn diagrams, although it’s not the cheapest thing around.

Leave a comment Cancel reply

Please enter an answer in digits: one × four =

Download our all-new eBook for tips on 50 powerful Business Diagrams for Strategic Planning.

• HW Guidelines
• Study Skills Quiz
• Find Local Tutors
• Demo MathHelp.com
• Join MathHelp.com

Select a Course Below

• ACCUPLACER Math
• Math Placement Test
• PRAXIS Math
• + more tests
• 5th Grade Math
• 6th Grade Math
• Pre-Algebra
• College Pre-Algebra
• Introductory Algebra
• Intermediate Algebra
• College Algebra

Venn Diagrams: Exercises

Intro Set Not'n Sets Exercises Diag. Exercises

Venn diagram word problems generally give you two or three classifications and a bunch of numbers. You then have to use the given information to populate the diagram and figure out the remaining information. For instance:

Out of forty students, 14 are taking English Composition and 29 are taking Chemistry.

• If five students are in both classes, how many students are in neither class?
• How many are in either class?
• What is the probability that a randomly-chosen student from this group is taking only the Chemistry class?

Content Continues Below

MathHelp.com

There are two classifications in this universe: English students and Chemistry students.

First I'll draw my universe for the forty students, with two overlapping circles labelled with the total in each:

(Well, okay; they're ovals, but they're always called "circles".)

Five students are taking both classes, so I'll put " 5 " in the overlap:

I've now accounted for five of the 14 English students, leaving nine students taking English but not Chemistry, so I'll put " 9 " in the "English only" part of the "English" circle:

I've also accounted for five of the 29 Chemistry students, leaving 24 students taking Chemistry but not English, so I'll put " 24 " in the "Chemistry only" part of the "Chemistry" circle:

This tells me that a total of 9 + 5 + 24 = 38 students are in either English or Chemistry (or both). This gives me the answer to part (b) of this exercise. This also leaves two students unaccounted for, so they must be the ones taking neither class, which is the answer to part (a) of this exercise. I'll put " 2 " inside the box, but outside the two circles:

The last part of this exercise asks me for the probability that a agiven student is taking Chemistry but not English. Out of the forty students, 24 are taking Chemistry but not English, which gives me a probability of:

24/40 = 0.6 = 60%

• Two students are taking neither class.
• There are 38 students in at least one of the classes.
• There is a 60% probability that a randomly-chosen student in this group is taking Chemistry but not English.

Years ago, I discovered that my (now departed) cat had a taste for the adorable little geckoes that lived in the bushes and vines in my yard, back when I lived in Arizona. In one month, suppose he deposited the following on my carpet:

• six gray geckoes,
• twelve geckoes that had dropped their tails in an effort to escape capture, and
• fifteen geckoes that he'd chewed on a little

In addition:

• only one of the geckoes was gray, chewed-on, and tailless;
• two were gray and tailless but not chewed-on;
• two were gray and chewed-on but not tailless.

If there were a total of 24 geckoes left on my carpet that month, and all of the geckoes were at least one of "gray", "tailless", and "chewed-on", how many were tailless and chewed-on, but not gray?

If I work through this step-by-step, using what I've been given, I can figure out what I need in order to answer the question. This is a problem that takes some time and a few steps to solve.

They've given me that each of the geckoes had at least one of the characteristics, so each is a member of at least one of the circles. This means that there will be nothing outside of the circles; the circles will account for everything in this particular universe.

There was one gecko that was gray, tailless, and chewed on, so I'll draw my Venn diagram with three overlapping circles, and I'll put " 1 " in the center overlap:

Two of the geckoes were gray and tailless but not chewed-on, so " 2 " goes in the rest of the overlap between "gray" and "tailless".

Two of them were gray and chewed-on but not tailless, so " 2 " goes in the rest of the overlap between "gray" and "chewed-on".

Since a total of six were gray, and since 2 + 1 + 2 = 5 of these geckoes have already been accounted for, this tells me that there was only one left that was only gray.

This leaves me needing to know how many were tailless and chewed-on but not gray, which is what the problem asks for. But, because I don't know how many were only chewed on or only tailless, I cannot yet figure out the answer value for the remaining overlap section.

I need to work with a value that I don't yet know, so I need a variable. I'll let " x " stand for this unknown number of tailless, chewed-on geckoes.

I do know the total number of chewed geckoes ( 15 ) and the total number of tailless geckoes ( 12 ). After subtracting, this gives me expressions for the remaining portions of the diagram:

only chewed on:

15 − 2 − 1 − x = 12 − x

only tailless:

12 − 2 − 1 − x = 9 − x

There were a total of 24 geckoes for the month, so adding up all the sections of the diagram's circles gives me: (everything from the "gray" circle) plus (the unknown from the remaining overlap) plus (the only-chewed-on) plus (the only-tailless), or:

(1 + 2 + 1 + 2) + ( x )

+ (12 − x ) + (9 − x )

= 27 − x = 24

Solving , I get x = 3 . So:

Three geckoes were tailless and chewed on but not gray.

(No geckoes or cats were injured during the production of the above word problem.)

For more word-problem examples to work on, complete with worked solutions, try this page provided by Joe Kahlig of Texas A&M University. There is also a software package (DOS-based) available through the Math Archives which can give you lots of practice with the set-theory aspect of Venn diagrams. The program is not hard to use, but you should definitely read the instructions before using.

URL: https://www.purplemath.com/modules/venndiag4.htm

Page 1 Page 2 Page 3 Page 4

Standardized Test Prep

College math, homeschool math, share this page.

• Terms of Use
• About Purplemath
• About the Author
• Tutoring from PM
• Advertising
• Linking to PM
• Site licencing

Visit Our Profiles

Venn Diagrams Practice Questions

Click here for questions, click here for answers, gcse revision cards.

5-a-day Workbooks

Primary Study Cards

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

Set Theory: Venn Diagrams And Subsets

Related Pages Union Of Sets Intersection Of Two Sets Intersection Of Three Sets More Lessons On Sets More Lessons for GCSE Maths Math Worksheets

What Is A Venn Diagram?

A Venn Diagram is a pictorial representation of the relationships between sets.

We can represent sets using Venn diagrams . In a Venn diagram, the sets are represented by shapes; usually circles or ovals. The elements of a set are labeled within the circle.

The following diagrams show the set operations and Venn Diagrams for Complement of a Set, Disjoint Sets, Subsets, Intersection and Union of Sets. Scroll down the page for more examples and solutions.

The set of all elements being considered is called the Universal Set (U) and is represented by a rectangle.

• The complement of A, A’ , is the set of elements in U but not in A. A’ ={ x | x ∈ U and x ∉ A}
• Sets A and B are disjoint sets if they do not share any common elements.
• B is a proper subset of A. This means B is a subset of A, but B ≠ A.
• The intersection of A and B is the set of elements in both set A and set B. A ∩ B = { x | x ∈ A and x ∈ B}
• The union of A and B is the set of elements in set A or set B. A ∪ B = { x | x ∈ A or x ∈ B}

Set Operations And Venn Diagrams

Example: 1. Create a Venn Diagram to show the relationship among the sets. U is the set of whole numbers from 1 to 15. A is the set of multiples of 3. B is the set of primes. C is the set of odd numbers.

2. Given the following Venn Diagram determine each of the following set. a) A ∩ B b) A ∪ B c) (A ∪ B)’ d) A’ ∩ B e) A ∪ B'

Venn Diagram Examples

Example: Given the set P is the set of even numbers between 15 and 25. Draw and label a Venn diagram to represent the set P and indicate all the elements of set P in the Venn diagram.

Solution: List out the elements of P . P = {16, 18, 20, 22, 24} ← ‘between’ does not include 15 and 25 Draw a circle or oval. Label it P . Put the elements in P .

Example: Draw and label a Venn diagram to represent the set R = {Monday, Tuesday, Wednesday}.

Solution: Draw a circle or oval. Label it R . Put the elements in R .

Example: Given the set Q = { x : 2 x – 3 < 11, x is a positive integer }. Draw and label a Venn diagram to represent the set Q .

Solution: Since an equation is given, we need to first solve for x . 2 x – 3 < 11 ⇒ 2 x < 14 ⇒ x < 7

So, Q = {1, 2, 3, 4, 5, 6} Draw a circle or oval. Label it Q . Put the elements in Q .

Venn Diagram Videos

What’s a Venn Diagram, and What Does Intersection and Union Mean?

Venn Diagram and Subsets

Learn about Venn diagrams and subsets.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Learn maths at home

How to Solve Venn Diagrams with 3 Circles

Venn diagrams with 3 circles: video lesson, what is the purpose of venn diagrams.

A Venn diagram is a type of graphical organizer which can be used to display similarities and differences between two or more sets. Circles are used to represent each set and any properties in common to both sets will be written in the overlap of the circles. Any property unique to a particular set is written in that circle alone.

For example, here is a Venn diagram comparing and contrasting dogs and cats.

The Venn diagram shows the following information:

• Have non-retractable claws
• Have round pupils
• Roam the street
• Have retractable claws
• Have slit pupils

Both dogs and cats:

• Can be pets
• Have 4 legs

A Venn diagram with three circles is called a triple Venn diagram.

A Venn diagram with three circles is used to compare and contract three categories. Each circle represents a different category with the overlapping regions used to represent properties that are shared between the three categories.

For example, a triple Venn diagram with 3 circles is used to compare dogs, cats and birds.

Dogs, cats and birds can all have claws and can also be pets.

Only birds:

• Have a beak
• Have 2 legs

Only both dogs and cats:

Only both dogs and birds:

Only both cats and birds:

• Don’t need walks

How to Make a Venn Diagram with 3 Circles

• Write the number of items belonging to all three sets in the central overlapping region.
• Write the remaining number of items belonging each pair of the sets in their overlapping regions.
• Write the remaining number of items belonging to each individual set in the non-overlapping region of each circle.

Make a Venn Diagram for the following situation:

30 students were asked which sports they play.

• 20 play basketball in total
• 16 play football in total
• 15 play tennis in total
• 10 play basketball and tennis
• 11 play basketball and football
• 9 play football and tennis
• 7 play all three

• Write the number of items belonging to all three sets in the central overlapping region

When making a Venn diagram, it is important to complete any overlapping regions first.

In this example, we start with the students that play all three sports. 7 students play all three sports.

The number 7 is placed in the overlap of all 3 circles. The shaded region shown is the overlapping area of all three circles.

2. Write the remaining number of items belonging each pair of the sets in their overlapping regions

There are 3 regions in which exactly two circles overlap.

There is the overlap of basketball and tennis, basketball and football and then tennis and football.

There are 10 students that play both basketball and tennis. The overlapping region of these two circles is shown below. We already have the 7 students that play all three sports in this region.

Therefore we only need 3 more students who play basketball and tennis but do not play football to make the total of this region add up to 10.

The next overlapping region of two circles is those that play basketball and football. There are 11 students in total that play both.

The overlapping region of the basketball and football circles is shown below.

There are already 7 students who play all three sports and so, a further 4 students must play both basketball and football but not tennis in order to make the total in this shaded region add up to 11 students.

The next overlapping region of two circles is those that play football and tennis. There are 9 students in total that play both.

The overlapping region of the football and tennis circles is shown below.

There are already 7 students who play all three sports and so, a further 2 students must play both football and tennis but not basketball in order to make the total in this shaded region add up to 9 students.

Write the remaining number of items belonging to each individual set in the non-overlapping region of each circle

There are three individual sets which are represented by the three circles. There are those that play basketball, football and tennis.

20 students play basketball in total. These 20 students are shown by the shaded circle below.

We already have 3, 7 and 4 students in the overlapping regions. This is a total of 14 students so far. We need a further 6 students who only play basketball in order for the numbers in this circle to make a total of 20.

The next individual sport is football. 16 students play football in total.

There are already 4, 7 and 2 students in the overlapping regions. This makes a total of 13 students so far.

3 more students are required to make the circle total up to 16. 3 students play only football and not basketball and tennis.

Finally, there are 15 students who play tennis shown by the shaded region below.

There are already 3, 7 and 2 students in the overlapping regions, making a total of 12 students.

A further 3 students are required to make the total of 15 students in this circle.

3 students play tennis but not basketball or football.

The values in each circle sum to 28 students.

That is 6 + 4 + 3 + 7 + 3 + 2 + 3 = 28.

Since there are 30 students who were asked in total, a further 2 students must play none of these three sports.

How to Solve a Venn Diagram with 3 Circles

To solve a Venn diagram with 3 circles, start by entering the number of items in common to all three sets of data. Then enter the remaining number of items in the overlapping region of each pair of sets. Enter the remaining number of items in each individual set. Finally, use any known totals to find missing numbers.

Venn diagrams are particularly useful for solving word problems in which a list of information is given about different categories. Numbers are placed in each region representing each statement.

100 people were asked which pets they have.

• 32 people in total have a cat
• 18 people in total have a rabbit
• 10 people have just a dog and a rabbit
• 21 people have just a dog and a cat
• 7 people have just a cat and a rabbit
• 3 people own all three pets

How many people just have a dog?

Start by entering the number of items in common to all three sets of data

3 people own all three pets and so, a number 3 is written in the overlapping region of all three circles.

Then enter the remaining number of items in the overlapping region of each pair of sets

10 people have just a dog and a rabbit.

Since 3 people are already in this region, 7 more people are needed.

21 people have just a dog and a cat.

Since 3 people are already in this region, 18 more people are needed.

7 people have just a cat and a rabbit.

Since 3 people are already in this region, 4 more people are needed.

Enter the remaining number of items in each individual set

32 people in total have a cat.

There are already 18 + 3 + 4 = 25 people in this circle.

Therefore a further 7 people are needed in this circle to make 32.

7 people just own a cat and no other pet.

18 people in total have a rabbit.

There are already 7 + 3 + 4 = 14 people in this circle.

Therefore a further 4 people are needed in this circle to make 18.

4 people just own a rabbit and no other pet.

Finally, use any known totals to find missing numbers

We are now told that 25 people own none of these pets. This means that a 25 is written outside of all of the circles but still within the Venn diagram.

The question requires the number of people who just own a dog.

There are 100 people in total and so, all of the numbers in the complete Venn diagram must add up to 100.

Adding the numbers so far, 3 + 7 + 4 + 18 + 4 + 7 + 25 = 68 people in total.

Since the numbers must add to 100, there must be a further 32 people who own a dog.

Now all of the numbers in the Venn diagram add to 100.

Venn Diagram with 3 Circles Template

Here is a downloadable template for a blank Venn Diagram with 3 circles.

How to Shade a Venn Diagram with 3 Circles

Here are some examples of shading Venn diagrams with 3 sets:

Shaded Region: A

Shaded Region: B

Shaded Region: C

Shaded Region: A∪B

Shaded Region: B∪C

Shaded Region: A∪C

Shaded Region: A∩B

Shaded Region: B∩C

Shaded Region: A∩C

Shaded Region: A∪B∪C

Shaded Region: A∩B∩C

Shaded Region: (A∩B)∪(A∩C)

• Testimonial
• Web Stories

Learning Home

Not Now! Will rate later

Venn Diagram: Concept and Solved Questions

What is a Venn Diagram?

Venn diagram, also known as Euler-Venn diagram is a simple representation of sets by diagrams. The usual depiction makes use of a rectangle as the universal set and circles for the sets under consideration.

In CAT and other MBA entrance exams, questions asked from this topic involve 2 or 3 variable only. Therefore, in this article we are going to discuss problems related to 2 and 3 variables.

Let's take a look at some basic formulas for Venn diagrams of two and three elements.

n ( A ∪ B) = n(A ) + n ( B ) - n ( A∩ B) n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) - n ( A ∩ B) - n ( B ∩ C) - n ( C ∩ A) + n (A ∩ B ∩ C )

And so on, where n( A) = number of elements in set A.  Once you understand the concept of Venn diagram with the help of diagrams, you don’t have to memorize these formulas.

Venn Diagram in case of two elements

Where;  X = number of elements that belong to set A only Y = number of elements that belong to set B only Z = number of elements that belong to set A and B both (AB) W = number of elements that belong to none of the sets A or B From the above figure, it is clear that  n(A) = x + z ;  n (B) = y + z ;  n(A ∩ B) = z; n ( A ∪ B) = x +y+ z. Total number of elements = x + y + z + w

• CAT Admit Card
• CAT Eligibility Criteria
• CAT Exam Pattern
• CAT Preparation
• CAT Registration
• CAT 2019 Analysis
• CAT Study Material
• CAT 2021 Crash Course
• CAT 2023 Analysis
• B-School Application Form
• CAT Percentile Predictor
• MBA College Counselling
• CAT Notification
• CAT Syllabus
• CAT Question Papers
• CAT Sample Papers
• CAT Mock Test
• CAT Test Series
• CAT Cut Off
• CAT Colleges
• CAT Online Coaching

Venn Diagram in case of three elements

Where, W = number of elements that belong to none of the sets A, B or C

Tip: Always start filling values in the Venn diagram from the innermost value.

Solved Examples

Example 1:  In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee. 

• How many students like only tea?
• How many students like only coffee?
• How many students like neither tea nor coffee?
• How many students like only one of tea or coffee?
• How many students like at least one of the beverages?

Solution:  The given information may be represented by the following Venn diagram, where T = tea and C = coffee.

• Number of students who like only tea = 60
• Number of students who like only coffee = 40
• Number of students who like neither tea nor coffee = 20
• Number of students who like only one of tea or coffee = 60 + 40 = 100
• Number of students who like at least one of tea or coffee = n (only Tea) + n (only coffee) + n (both Tea & coffee) = 60 + 40 + 80 = 180

Example 2:  In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basket ball both. 5% liked watching none of these games.

• How many students like watching all the three games?
• Find the ratio of number of students who like watching only football to those who like watching only hockey.
• Find the number of students who like watching only one of the three given games.
• Find the number of students who like watching at least two of the given games.

Solution: n(F) = percentage of students who like watching football = 49% n(H) = percentage of students who like watching hockey = 53% n(B)= percentage of students who like watching basketball = 62% n ( F ∩ H) = 27% ; n (B ∩ H) = 29% ; n(F ∩ B) = 28% Since 5% like watching none of the given games so, n (F ∪ H ∪ B) = 95%. Now applying the basic formula, 95% = 49% + 53% + 62% -27% - 29% - 28% + n (F ∩ H ∩ B) Solving, you get n (F ∩ H ∩ B) = 15%.

Now, make the Venn diagram as per the information given. Note: All values in the Venn diagram are in percentage.

• Number of students who like watching all the three games = 15 % of 500 = 75.
• Ratio of the number of students who like only football to those who like only hockey = (9% of 500)/(12% of 500) = 9/12 = 3:4.
• The number of students who like watching only one of the three given games = (9% + 12% + 20%) of 500 = 205
• The number of students who like watching at least two of the given games=(number of students who like watching only two of the games) +(number of students who like watching all the three games)= (12 + 13 + 14 + 15)% i.e. 54% of 500 = 270.

To know the importance of this topic, check out some previous year CAT questions from this topic:

CAT 2017 Solved Questions:

Solution:  It is given that 200 candidates scored above 90th percentile overall in CET. Let the following Venn diagram represent the number of persons who scored above 80 percentile in CET in each of the three sections:

2.  From the given condition, g is a multiple of 5. Hence, g = 20. The number of candidates at or above 90th percentile overall and at or above 80th percentile in both P and M = e + g = 60.

3.  In this case, g = 20. Number of candidates shortlisted for AET = d + e + f + g = 10 + 40 + 100 + 20 = 170

4.  From the given condition, the number of candidates at or above 90th percentile overall and at or above 80th percentile in P in CET = 104. The number of candidates who have to sit for separate test = 296 + 3 = 299.

Another type of questions asked from this topic is based on maxima and minima. We have discussed this type in the other article.

Key Learning:

• It is important to carefully list the conditions given in the question in the form of a Venn diagram.
• While solving such questions, avoid taking many variables.
• Try solving the questions using the Venn diagram approach and not with the help of formulae.

You can also post in the comment section below, any query or explanation for any concept mentioned in the article.

• CAT Logical Reasoning
• CAT Reading Comprehension
• CAT Grammar
• CAT Para Jumbles
• CAT Data Interpretation
• CAT Data Sufficiency
• CAT DI Questions
• CAT Analytical Reasoning

Most Popular Articles - PS

All About the Quantitative Aptitude of CAT

Number System for CAT Made Easy

100 Algebra Questions Every CAT Aspirant Must Solve

Use Creativity to crack CAT

Averages: Finding the Missing Page Number

Strategy for Quant Questions in CAT

Comprehensive Guide for CAT Probability

Comprehensive Guide for CAT Mensuration

Chess Board: How to find Number of Squares and Rectangles

100 Geometry questions every CAT aspirant must solve

Permutation and Combination and Probability for CAT

Tackle Time, Speed & Distance for CAT

Sequences and Series - Advanced

CAT Formulae E-Book

Races and Games

Geometry: Shortcuts and Tricks

Number System-Integral Solutions: Shortcuts and Tricks

Permutation and Combination: Advanced

Geometry - Polygons

Number System: Integral Solutions and Remainders based on Factorials

How to improve in Geometry & Mensuration

How to improve in Permutation and Combination

Cheat Codes: Permutation and Combination

How to improve in Algebra

• + ACCUPLACER Mathematics
• + ACT Mathematics
• + AFOQT Mathematics
• + ALEKS Tests
• + ASVAB Mathematics
• + ATI TEAS Math Tests
• + Common Core Math
• + DAT Math Tests
• + FSA Tests
• + FTCE Math
• + GED Mathematics
• + Georgia Milestones Assessment
• + GRE Quantitative Reasoning
• + HiSET Math Exam
• + HSPT Math
• + ISEE Mathematics
• + PARCC Tests
• + Praxis Math
• + PSAT Math Tests
• + PSSA Tests
• + SAT Math Tests
• + SBAC Tests
• + SIFT Math
• + SSAT Math Tests
• + STAAR Tests
• + TABE Tests
• + TASC Math
• + TSI Mathematics
• + ACT Math Worksheets
• + Accuplacer Math Worksheets
• + AFOQT Math Worksheets
• + ALEKS Math Worksheets
• + ASVAB Math Worksheets
• + ATI TEAS 6 Math Worksheets
• + FTCE General Math Worksheets
• + GED Math Worksheets
• + 3rd Grade Mathematics Worksheets
• + 4th Grade Mathematics Worksheets
• + 5th Grade Mathematics Worksheets
• + 6th Grade Math Worksheets
• + 7th Grade Mathematics Worksheets
• + 8th Grade Mathematics Worksheets
• + 9th Grade Math Worksheets
• + HiSET Math Worksheets
• + HSPT Math Worksheets
• + ISEE Middle-Level Math Worksheets
• + PERT Math Worksheets
• + Praxis Math Worksheets
• + PSAT Math Worksheets
• + SAT Math Worksheets
• + SIFT Math Worksheets
• + SSAT Middle Level Math Worksheets
• + 7th Grade STAAR Math Worksheets
• + 8th Grade STAAR Math Worksheets
• + THEA Math Worksheets
• + TABE Math Worksheets
• + TASC Math Worksheets
• + TSI Math Worksheets
• + AFOQT Math Course
• + ALEKS Math Course
• + ASVAB Math Course
• + ATI TEAS 6 Math Course
• + CHSPE Math Course
• + FTCE General Knowledge Course
• + GED Math Course
• + HiSET Math Course
• + HSPT Math Course
• + ISEE Upper Level Math Course
• + SHSAT Math Course
• + SSAT Upper-Level Math Course
• + PERT Math Course
• + Praxis Core Math Course
• + SIFT Math Course
• + 8th Grade STAAR Math Course
• + TABE Math Course
• + TASC Math Course
• + TSI Math Course
• + Number Properties Puzzles
• + Algebra Puzzles
• + Geometry Puzzles
• + Intelligent Math Puzzles
• + Ratio, Proportion & Percentages Puzzles
• + Other Math Puzzles

How to Solve Problems Using Venn Diagrams

Venn diagrams are visual tools often used to organize and understand sets and the relationships between them. They're named after John Venn, a British philosopher, and logician who introduced them in the 1880s. Venn diagrams are frequently used in various fields, including mathematics, statistics, logic, computer science, etc. They're handy for solving problems involving sets and subsets, intersections, unions, and complements.

A Step-by-step Guide to Solving Problems Using Venn Diagrams

Here’s a step-by-step guide on how to solve problems using Venn diagrams:

Step 1: Understand the Problem

As with any problem-solving method, the first step is to understand the problem. What sets are involved? How are they related? What are you being asked to find?

Step 2: Draw the Diagram

Draw a rectangle to represent the universal set, which includes all possible elements. Each set within the universal set is represented by a circle. If there are two sets, draw two overlapping circles. If there are three sets, draw three overlapping circles, and so forth. Each section in the overlapping circles represents different intersections of the sets.

Step 3: Label the Diagram

Each circle (set) should be labeled appropriately. If you’re dealing with sets of different types of fruits, for example, one might be labeled “Apples” and another “Oranges”.

Step 4: Fill in the Values

Start filling in the values from the innermost part of the diagram (where all sets overlap) to the outer parts. This helps to avoid double-counting elements that belong to more than one set. Information provided in the problem usually tells you how many elements are in each set or section.

Step 5: Solve the Problem

Now, you can use the diagram to answer the question. This might involve counting the number of elements in a particular set or section of the diagram, or it might involve noticing patterns or relationships between the sets.

Step 6: Check Your Answer

Make sure your answer makes sense in the context of the problem and that you’ve accounted for all elements in the diagram.

by: Effortless Math Team about 1 year ago (category: Articles )

Effortless Math Team

Related to this article, more math articles.

• Top 10 4th Grade MEAP Math Practice Questions
• FREE 6th Grade SBAC Math Practice Test
• Full-Length 7th Grade PSSA Math Practice Test
• What is the Relationship Between Arcs and Central Angles?
• What Kind of Math Is on the PSAT/NMSQT Test?
• 5 Skills You Need to Study Mathematics in College
• Theoretical and Empirical Probability Distributions
• Top 10 HiSET Math Practice Questions
• 7th Grade Georgia Milestones Assessment System Math Worksheets: FREE & Printable
• Top 10 Tips to Overcome PERT Math Anxiety

What people say about "How to Solve Problems Using Venn Diagrams - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

Leave a Reply Cancel reply

You must be logged in to post a comment.

Mastering Grade 6 Math Word Problems The Ultimate Guide to Tackling 6th Grade Math Word Problems

Mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems, mastering grade 2 math word problems the ultimate guide to tackling 2nd grade math word problems, mastering grade 8 math word problems the ultimate guide to tackling 8th grade math word problems, mastering grade 4 math word problems the ultimate guide to tackling 4th grade math word problems, mastering grade 3 math word problems the ultimate guide to tackling 3rd grade math word problems.

• ATI TEAS 6 Math
• ISEE Upper Level Math
• SSAT Upper-Level Math
• Praxis Core Math
• 8th Grade STAAR Math

Limited time only!

Save Over 45 %

It was $89.99 now it is $49.99

Login and use all of our services.

Effortless Math services are waiting for you. login faster!

Register Fast!

Password will be generated automatically and sent to your email.

After registration you can change your password if you want.

• Math Worksheets
• Math Courses
• Math Topics
• Math Puzzles
• Math eBooks
• GED Math Books
• HiSET Math Books
• ACT Math Books
• ISEE Math Books
• ACCUPLACER Books
• Premium Membership
• Youtube Videos

Effortless Math provides unofficial test prep products for a variety of tests and exams. All trademarks are property of their respective trademark owners.

• Bulk Orders
• Refund Policy

• Pre-algebra lessons
• Pre-algebra word problems
• Algebra lessons
• Algebra word problems
• Algebra proofs
• Advanced algebra
• Geometry lessons
• Geometry word problems
• Geometry proofs
• Trigonometry lessons
• Consumer math
• Baseball math
• Math for nurses
• Statistics made easy
• High school physics
• Basic mathematics store
• SAT Math Prep
• Math skills by grade level
• Ask an expert
• Other websites
• K-12 worksheets
• Worksheets generator
• Algebra worksheets
• Geometry worksheets
• Free math problem solver
• Pre-algebra calculators
• Algebra Calculators
• Geometry Calculators
• Math puzzles
• Math tricks
• Member login

Venn diagram word problems

The Venn diagram word problems in this lesson will show you how to use Venn diagrams with 2 circles to solve problems involving counting. 

Venn diagram word problems with two circles

Word problem #1

A survey was conducted in a neighborhood with 128 families. The survey revealed the following information.

• 106 of the families have a credit card
• 73 of the families are trying to pay off a car loan
• 61 of the families have both a credit card and a car loan

Answer the following questions:

1. How many families have only a credit card?

2.  How many families have only a car loan?

3. How many families have neither a credit card nor a car loan?

4. How many families do not have a credit card?

5. How many families do not have a car loan?

6. How many families have a credit card or a car loan?

• Let C be families with a credit card
• Let L be families with a car loan
• Let S be the total number of families

The Venn diagram above can be used to answer all these questions. 

Tips on how to create the Venn diagram. Always put  first , in the middle or in the intersection, the value that is in both sets. For example, since 61 families have both a credit card and a car loan, put 61 in the intersection before you do anything else. In C only, put 45 since 106 - 61 = 45

In L only, put 12 since 73 - 61 = 12

Outside C and L, put 10 since 128 - 61 - 45 - 12 = 10

The expression, " only a credit card" means that it is only in C. Any number in L cannot be included. 1.  The number of families with only a credit card is 45. Do not add 61 to 45 since 61 is in L.

2.  The number of families with only a car loan is 12. 

3. The number of families with neither a credit card nor a car loan is 10. 10 is not in C nor in L.

4. The number families without a credit card is found by adding everything that is not in C. 12 + 10 = 22

5.  The number families without a car loan is found by adding everything that is not in L. 45 + 10 = 55

6. The number of families with a credit card or a car loan is found by adding anything in C only, in L only and in the intersection of C and L?

45 + 61 + 12 = 118

Word problem #2

A survey conducted in a school with 150 students revealed the following information:

• 78 students are enrolled in swimming class
• 85 students are enrolled in basketball class
• 25 are enrolled in both swimming and basketball class

1.  How many students are enrolled only in swimming class?

2.  How many students are enrolled only in basketball class?

3.  How many students are neither enrolled in swimming class nor basketball class?

4.  How many students are not enrolled in swimming class?

5.  How many students are not enrolled in basketball class?

6. How many students are enrolled in swimming class or basketball class?

• Let S be students enrolled in swimming class
• Let B be students enrolled in basketball class
• Let E be the total number of students

Using the same technique as in problem #1 , we have the following Venn diagram

1. The number of students enrolled only in swimming class is 53 2.  The number of students enrolled only in basketball class is 60

3. The number of students who are neither enrolled in swimming class nor basketball class is 12

4. Students not enrolled in swimming class are enrolled in basketball class only or are enrolled in neither of these two activities. In other words, everything that is not in S.

60 + 12 = 72

5.  Students not enrolled in basketball class are enrolled in swimming class only or are  enrolled in neither of these two activities. In other words, everything that is not in B.

53 + 12 = 65

6.  The number of students enrolled in swimming class or basketball class is found by adding anything in S only, in B only and in the intersection of S and B?

53 + 25 + 60 = 138

A tricky Venn diagram word problem with two circles

Word problem #3

In a survey of 100 people, 28 people smoke, 65 people drink, and 30 people do neither. How many people do both?

• Let K be the number of people who smoke
• Let D be  the number of people who drink
• Let E be the total number of people
• Let x be the number of people who smoke and drink

If we make a Venn diagram, here is what we have so far.

We end up with the following equation to solve for x.

(65 - x) + x + (28 - x) + 30 = 100

65 - x + x + 28 - x + 30 - 30 = 100 - 30

65 - x + x + 28 - x  = 70

65 + 0 + 28 - x  = 70

93 - x  = 70

Since 93 - 23 = 70, x  = 23

The number of people who do both is 23.

3-circle Venn diagram

Recent Articles

How to divide any number by 5 in 2 seconds.

Feb 28, 24 11:07 AM

Math Trick to Square Numbers from 50 to 59

Feb 23, 24 04:46 AM

Sum of Consecutive Odd Numbers

Feb 22, 24 10:07 AM

100 Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius!

 Recommended

About me :: Privacy policy :: Disclaimer :: Donate   Careers in mathematics  

Copyright © 2008-2021. Basic-mathematics.com. All right reserved

Venn Diagram

A Venn diagram is used to visually represent the differences and the similarities between two concepts. Venn diagrams are also called logic or set diagrams and are widely used in set theory, logic, mathematics, businesses, teaching, computer science, and statistics.

Let's learn about Venn diagrams, their definition, symbols, and types with solved examples.

What is a Venn Diagram?

A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.

Venn Diagram Example

Let us observe a Venn diagram example. Here is the Venn diagram that shows the correlation between the following set of numbers.

• One set contains even numbers from 1 to 25 and the other set contains the numbers in the 5x table from 1 to 25.
• The intersecting part shows that 10 and 20 are both even numbers and also multiples of 5 between 1 to 25.

Terms Related to Venn Diagram

Let us understand the following terms and concepts related to Venn Diagram, to understand it better.

Universal Set

Whenever we use a set, it is easier to first consider a larger set called a universal set that contains all of the elements in all of the sets that are being considered. Whenever we draw a Venn diagram:

• A large rectangle is used to represent the universal set and it is usually denoted by the symbol E or sometimes U.
• All the other sets are represented by circles or closed figures within this larger rectangle .
• Every set is the subset of the universal set U.

Consider the above-given image:

• U is the universal set with all the numbers 1-10, enclosed within the rectangle.
• A is the set of even numbers 1-10, which is the subset of the universal set U and it is placed inside the rectangle.
• All the numbers between 1-10, that are not even, will be placed outside the circle and within the rectangle as shown above.

Venn diagrams are used to show subsets. A subset is actually a set that is contained within another set. Let us consider the examples of two sets A and B in the below-given figure. Here, A is a subset of B. Circle A is contained entirely within circle B. Also, all the elements of A are elements of set B.

This relationship is symbolically represented as A ⊆ B. It is read as A is a subset of B or A subset B. Every set is a subset of itself. i.e. A ⊆ A. Here is another example of subsets :

• N = set of natural numbers
• I = set of integers
• Here N ⊂ I, because all-natural numbers are integers .

Venn Diagram Symbols

There are more than 30 Venn diagram symbols. We will learn about the three most commonly used symbols in this section. They are listed below as:

Let us understand the concept and the usage of the three basic Venn diagram symbols using the image given below.

Venn Diagram for Sets Operations

In set theory, we can perform certain operations on given sets. These operations are as follows,

• Union of Set
• Intersection of set
• Complement of set
• Difference of set

Union of Sets Venn Diagram

The union of two sets A and B can be given by: A ∪ B = {x | x ∈ A or x ∈ B}. This operation on the elements of set A and B can be represented using a Venn diagram with two circles. The total region of both the circles combined denotes the union of sets A and B.

Intersection of Set Venn Diagram

The intersection of sets, A and B is given by: A ∩ B = {x : x ∈ A and x ∈ B}. This operation on set A and B can be represented using a Venn diagram with two intersecting circles. The region common to both the circles denotes the intersection of set A and Set B.

Complement of Set Venn Diagram

The complement of any set A can be given as A'. This represents elements that are not present in set A and can be represented using a Venn diagram with a circle. The region covered in the universal set, excluding the region covered by set A, gives the complement of A.

Difference of Set Venn Diagram

The difference of sets can be given as, A - B. It is also referred to as a ‘relative complement’. This operation on sets can be represented using a Venn diagram with two circles. The region covered by set A, excluding the region that is common to set B, gives the difference of sets A and B.

We can observe the above-explained operations on sets using the figures given below,

Venn Diagram for Three Sets

Three sets Venn diagram is made up of three overlapping circles and these three circles show how the elements of the three sets are related. When a Venn diagram is made of three sets, it is also called a 3-circle Venn diagram. In a Venn diagram, when all these three circles overlap, the overlapping parts contain elements that are either common to any two circles or they are common to all the three circles. Let us consider the below given example:

Here are some important observations from the above image:

• Elements in P and Q = elements in P and Q only plus elements in P, Q, and R.
• Elements in Q and R = elements in Q and R only plus elements in P, Q, and R.
• Elements in P and R = elements in P and R only plus elements in P, Q, and R.

How to Draw a Venn Diagram?

Venn diagrams can be drawn with unlimited circles. Since more than three becomes very complicated, we will usually consider only two or three circles in a Venn diagram. Here are the 4 easy steps to draw a Venn diagram:

• Step 1: Categorize all the items into sets.
• Step 2: Draw a rectangle and label it as per the correlation between the sets.
• Step 3: Draw the circles according to the number of categories you have.
• Step 4: Place all the items in the relevant circles.

Example: Let us draw a Venn diagram to show categories of outdoor and indoor for the following pets: Parrots, Hamsters, Cats, Rabbits, Fish, Goats, Tortoises, Horses.

• Step 1: Categorize all the items into sets (Here, its pets): Indoor pets: Cats, Hamsters, and, Parrots. Outdoor pets: Horses, Tortoises, and Goats. Both categories (outdoor and indoor): Rabbits and Fish.
• Step 2: Draw a rectangle and label it as per the correlation between the two sets. Here, let's label the rectangle as Pets.
• Step 3: Draw the circles according to the number of categories you have. There are two categories in the sample question: outdoor pets and indoor pets. So, let us draw two circles and make sure the circles overlap.

• Step 4: Place all the pets in the relevant circles. If there are certain pets that fit both the categories, then place them at the intersection of sets , where the circles overlap. Rabbits and fish can be kept as indoor and outdoor pets, and hence they are placed at the intersection of both circles.

• Step 5: If there is a pet that doesn't fit either the indoor or outdoor sets, then place it within the rectangle but outside the circles.

Venn Diagram Formula

For any two given sets A and B, the Venn diagram formula is used to find one of the following: the number of elements of A, B, A U B, or A ⋂ B when the other 3 are given. The formula says:

n(A U B) = n(A) + n(B) – n (A ⋂ B)

Here, n(A) and n(B) represent the number of elements in A and B respectively. n(A U B) and n(A ⋂ B) represent the number of elements in A U B and A ⋂ B respectively. This formula is further extended to 3 sets as well and it says:

• n (A U B U C) = n(A) + n(B) + n(C) - n(A ⋂ B) - n(B ⋂ C) - n(C ⋂ A) + n(A ⋂ B ⋂ C)

Here is an example of Venn diagram formula.

Example:  In a cricket school, 12 players like bowling, 15 like batting, and 5 like both. Then how many players like either bowling or batting.

Let A and B be the sets of players who like bowling and batting respectively. Then

n(A ⋂ B) = 5

We have to find n(A U B). Using the Venn diagram formula,

n(A U B) = 12 + 15 - 5 = 22.

Applications of Venn Diagram

There are several advantages to using Venn diagrams. Venn diagram is used to illustrate concepts and groups in many fields, including statistics, linguistics, logic, education, computer science, and business.

• We can visually organize information to see the relationship between sets of items, such as commonalities and differences, and to depict the relations for visual communication.
• We can compare two or more subjects and clearly see what they have in common versus what makes them different. This might be done for selecting an important product or service to buy.
• Mathematicians also use Venn diagrams in math to solve complex equations.
• We can use Venn diagrams to compare data sets and to find correlations .
• Venn diagrams can be used to reason through the logic behind statements or equations .

☛ Related Articles:

Check out the following pages related to Venn diagrams:

• Operations on Sets
• Roster Notation
• Set Builder Notation
• Probability

Important Notes on Venn Diagrams:

Here is a list of a few points that should be remembered while studying Venn diagrams:

• Every set is a subset of itself i.e., A ⊆ A.
• A universal set accommodates all the sets under consideration.
• If A ⊆ B and B ⊆ A, then A = B
• The complement of a complement is the given set itself.

Examples of Venn Diagram

Example 1: Let us take an example of a set with various types of fruits, A = {guava, orange, mango, custard apple, papaya, watermelon, cherry}. Represent these subsets using sets notation: a) Fruit with one seed b) Fruit with more than one seed

Solution: Among the various types of fruit, only mango and cherry have one seed.

Answer:    a) Fruit with one seed = {mango, cherry}  b) Fruit with more than one seed = {guava, orange, custard apple, papaya, watermelon}

Note:  If we represent these two sets on a Venn diagram, the intersection portion is empty.

Example 2: Let us take an example of two sets A and B, where A = {3, 7, 9} and B = {4, 8}. These two sets are subsets of the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Find A ∪ B.

Solution: The Venn diagram for the above relations can be drawn as:

Answer:  A ∪ B means, all the elements that belong to either set A or set B or both the sets = {3, 4, 7, 8, 9}

Example 3: Using Venn diagram, find X ∩ Y, given that X = {1, 3, 5}, Y = {2, 4, 6}.

Given: X = {1, 3, 5}, Y = {2, 4, 6}

The Venn diagram for the above example can be given as,

Answer:  From the blue shaded portion of Venn diagram, we observe that, X ∩ Y = ∅ ( null set ).

go to slide go to slide go to slide

Book a Free Trial Class

Venn Diagram Practice Questions

go to slide go to slide

FAQs on Venn Diagrams

What is a venn diagram in math.

In math, a Venn diagram is used to visualize the logical relationship between sets and their elements and helps us solve examples based on these sets.

How do You Read a Venn Diagram?

These are steps to be followed while reading a Venn diagram:

• First, observe all the circles that are present in the entire diagram.
• Every element present in a circle is its own item or data set.
• The intersecting or the overlapping portions of the circles contain the items that are common to the different circles.
• The parts that do not overlap or intersect show the elements that are unique to the different circle.

What is the Importance of Venn Diagram?

Venn diagrams are used in different fields including business, statistics, linguistics, etc. Venn diagrams can be used to visually organize information to see the relationship between sets of items, such as commonalities and differences, and to depict the relations for visual communication.

What is the Middle of a Venn Diagram Called?

When two or more sets intersect, overlap in the middle of a Venn diagram, it is called the intersection of a Venn diagram. This intersection contains all the elements that are common to all the different sets that overlap.

How to Represent a Universal Set Using Venn Diagram?

A large rectangle is used to represent the universal set and it is usually denoted by the symbol E or sometimes U. All the other sets are represented by circles or closed figures within this larger rectangle that represents the universal set.

What are the Different Types of Venn Diagrams?

The different types of Venn diagrams are:

• Two-set Venn diagram: The simplest of the Venn diagrams, that is made up of two circles or ovals of different sets to show their overlapping properties.
• Three-set Venn diagram: These are also called the three-circle Venn diagram, as they are made using three circles.
• Four-set Venn diagram: These are made out of four overlapping circles or ovals.
• Five-set Venn diagram: These comprise of five circles, ovals, or curves. In order to make a five-set Venn diagram, you can also pair a three-set diagram with repeating curves or circles.

What are the Different Fields of Applications of Venn Diagrams?

There are different cases of applications of Venn diagrams: Set theory, logic, mathematics, businesses, teaching, computer science, and statistics.

Can a Venn Diagram Have 2 Non Intersecting Circles?

Yes, a Venn digram can have two non intersecting circles where there is no data that is common to the categories belonging to both circles.

What is the Formula of Venn Diagram?

The formula that is very helpful to find the unknown information about a Venn diagram is n(A U B) = n(A) + n(B) – n (A ⋂ B), where

• A and B are two sets.
• n(A U B) is the number of elements in A U B.
• n (A ⋂ B) is the number of elements in A ⋂ B.

Can a Venn Diagram Have 3 Circles?

Yes, a Venn diagram can have 3 circles , and it's called a three-set Venn diagram to show the overlapping properties of the three circles.

What is Union in the Venn Diagram?

A union is one of the basic symbols used in the Venn diagram to show the relationship between the sets. A union of two sets C and D can be shown as C ∪ D, and read as C union D. It means, the elements belong to either set C or set D or both the sets.

What is A ∩ B Venn Diagram?

A ∩ B (which means A intersection B) in the Venn diagram represents the portion that is common to both the circles related to A and B.  A ∩ B can be a null set as well and in this case, the two circles will either be non-intersecting or can be represented with intersecting circles having no data in the intersection portion.

GCSE Tutoring Programme

"Our chosen students improved 1.19 of a grade on average - 0.45 more than those who didn't have the tutoring."

FREE GCSE Maths Resources

40+ GCSE maths papers (foundation & higher), 200+ worksheets, 15,000+ practice questions and more!

15 Venn Diagram Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

Beki Christian

Venn diagram questions involve visual representations of the relationship between two or more different groups of things. Venn diagrams are first covered in KS1 or KS2 and their complexity and uses progress through KS3 and KS4.

This blog will look at the types of Venn diagram questions possibly encountered at KS3 and KS4, focusing on exam-style example questions and in preparation for GCSEs. We will cover problem-solving questions and questions similar to those found in past papers. A worked example follows each question.

GCSE MATHS 2024: STAY UP TO DATE Join our email list to stay up to date with the latest news, revision lists and resources for GCSE maths 2024. We’re analysing each paper during the course of the 2024 GCSEs in order to identify the key topic areas to focus on for your revision. Thursday 16th May 2024: GCSE Maths Paper 1 2024 Analysis & Revision Topic List Monday 3rd June 2024: GCSE Maths Paper 2 2024 Analysis & Revision Topic List Monday 10th June 2024: GCSE Maths Paper 3 2024 Analysis GCSE 2024 dates GCSE 2024 results (when published) GCSE results 2023

How to solve Venn diagram questions

In KS3, sets and set notation are introduced when working with Venn diagrams. A set is a collection of objects. We identify a set using curly brackets. For example, if set \mathrm{A} contains the odd numbers between 1 and 10 , then we can write this as: A = \{1, 3, 5, 7, 9\}.

Venn diagrams sort objects, called elements, into two or more sets.

This diagram shows the set of elements \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} sorted into the following sets.

Set \mathrm{A} = factors of 10

Set \mathrm{B} = even numbers

The numbers in the overlap (intersection) belong to both sets. Those that are not in set \mathrm{A} or set \mathrm{B} are shown outside of the circles.

Different sections of a Venn diagram are denoted in different ways.

\xi represents the whole set, called the universal set.

\emptyset represents the empty set, a set containing no elements.

Let’s check out some other set notation examples!

In KS3 and KS4, we often use Venn diagrams to establish probabilities. We do this by reading information from the Venn diagram and applying the following formula.

For Venn diagrams we can say

15 Venn Diagram Questions & Practice Problems (KS3 & KS4) Worksheet

Download this free worksheet on Venn diagrams. This set of 15 Venn diagram questions and answer key will help you prepare for GCSE maths!

KS3 Venn diagram questions

In KS3, students learn to use set notation with Venn diagrams and start to find probabilities using Venn diagrams. The questions below are examples of questions that students may encounter in Years 7, Year 8 and Year 9.

Venn diagram questions Year 7

1. This Venn diagram shows information about the number of people who have brown hair and the number of people who wear glasses.

How many people have brown hair and glasses?

The intersection, where the Venn diagrams overlap, is the part of the Venn diagram which represents brown hair AND glasses. There are 4 people in the intersection.

2. Which set of objects is represented by the Venn diagram below?

We can see from the Venn diagram that there are two green triangles, one triangle that is not green, three green shapes that are not triangles and two shapes that are not green or triangles. These shapes belong to set D.

Venn diagram questions Year 8

3. Max asks 40 people whether they own a cat or a dog. 17 people own a dog, 14 people own a cat and 7 people own a cat and a dog. Choose the correct representation of this information on a Venn diagram.

There are 7 people who own a cat and a dog. Therefore, there must be 7 more people who own a cat, to make a total of 14 who own a cat, and 10 more people who own a dog, to make a total of 17 who own a dog.

Once we put this information on the Venn diagram, we can see that there are 7+7+10=24 people who own a cat, a dog or both.

40-24=16 , so there are 16 people who own neither.

4. The following Venn diagrams each show two sets, set \mathrm{A} and set \mathrm{B} . On which Venn diagram has \mathrm{A}^{\prime} been shaded?

\mathrm{A}^{\prime} means not in \mathrm{A} . This is shown in diagram \mathrm{B.}

Venn diagram questions Year 9

5. Place these values onto the following Venn diagram and use your diagram to find the number of elements in the set \text{S} \cup \text{O}.

\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \text{S} = square numbers \text{O} = odd numbers

\text{S} \cup \text{O} is the union of \text{S} or \text{O} , so it includes any element in \text{S} , \text{O} or both. The total number of elements in \text{S} , \text{O} or both is 6.

6. The Venn diagram below shows a set of numbers that have been sorted into prime numbers and even numbers.

A number is chosen at random. Find the probability that the number is prime and not even.

The section of the Venn diagram representing prime and not even is shown below.

There are 3 numbers in the relevant section out of a possible 10 numbers altogether. The probability, as a fraction, is \frac{3}{10}.

7. Some people visit the theatre. The Venn diagram shows the number of people who bought ice cream and drinks in the interval.

Ice cream is sold for £3 and drinks are sold for £2. A total of £262 is spent. How many people bought both a drink and an ice cream?

Money spent on drinks: 32 \times £2 = £64

Money spent on ice cream: 16 \times £3 = £48

£64+£4=£112 , so the information already on the Venn diagram represents £112 worth of sales.

£262-£112 = £150 , so another £150 has been spent.

If someone bought a drink and an ice cream, they would have spent £2+£3 = £5.  

£150 \div £5=30 , so 30 people bought a drink and an ice cream.

KS4 Venn diagram questions

At KS4, students are expected to be able to take information from word problems and put it onto a Venn diagram involving two or three sets. The use of set notation is extended and the probabilities become more complex. In the higher tier, Venn diagrams are used to calculate conditional probability.

Venn diagrams appear on exam papers across all exam boards, including Edexcel, AQA and OCR. Questions, particularly in the higher tier, may involve other areas of maths, such as percentages, ratio or algebra.

Foundation GCSE Venn diagram questions: grades 1-5

8. 50 people are asked whether they have been to France or Spain.

18 people have been to France. 23 people have been to Spain. 6 people have been to both.

By representing this information on a Venn diagram, find the probability that a person chosen at random has not been to Spain or France.

6 people have been to both France and Spain. This means 17 more have been to Spain to make 23 altogether, and 12 more have been to France to make 18 altogether. This makes 35 who have been to France, Spain or both and therefore 15 who have been to neither.

The probability that a person chosen at random has not been to France or Spain is \frac{15}{50}.

9. Some people were asked whether they like running, cycling or swimming. The results are shown in the Venn diagram below.

One person is chosen at random. What is the probability that the person likes running and cycling?

9 people like running and cycling (we include those who also like swimming) out of 80 people altogether. The probability that a person chosen at random likes running and cycling is \frac{9}{80}.

10. ξ = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16\}

\text{A} = \{ even numbers \}

\text{B} = \{ multiples of 3 \}

By completing the following Venn diagram, find \text{P}(\text{A} \cup \text{B}^{\prime}).

\text{A} \cup \text{B}^{\prime} means \text{A} or not \text{B} . We need to include everything that is in \text{A} or is not in \text{B} . There are 13 elements in \text{A} or not in \text{B} out of a total of 16 elements.

Therefore \text{P}(\text{A} \cup \text{B}^{\prime}) = \frac{13}{16}.

11. ξ = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}

A = \{ multiples of 2 \}

By putting this information onto the following Venn diagram, list all the elements of B.

We can start by placing the elements in \text{A} \cap \text{B} , which is the intersection.

We can then add any other multiples of 2 to set \text{A}.

Next, we can add any unused elements from \text{A} \cup \text{B} to \text{B}.

Finally, any other elements can be added to the outside of the Venn diagram.

The elements of \text{B} are \{1, 2, 3, 4, 6, 12\}.

Higher GCSE Venn diagram questions: grades 4-9

12. Some people were asked whether they like strawberry ice cream or chocolate ice cream. 82\% said they like strawberry ice cream and 70\% said they like chocolate ice cream. 4\% said they like neither.

By putting this information onto a Venn diagram, find the percentage of people who like both strawberry and chocolate ice cream.

Here, the percentages add up to 156\%. This is 56\% too much. In this total, those who like chocolate and strawberry have been counted twice and so 56\% is equal to the number who like both chocolate and strawberry. We can place 56\% in the intersection, \text{C} \cap \text{S}

We know that the total percentage who like chocolate is 70\%, so 70-56 = 14\%-14\% like just chocolate. Similarly, 82\% like strawberry, so 82-56 = 26\%-26\% like just strawberry.

13. The Venn diagram below shows some information about the height and gender of 40 students.

A student is chosen at random. Find the probability that the student is female given that they are over 1.2m.

We are told the student is over 1.2m. There are 20 students who are over 1.2m and 9 of them are female. Therefore the probability that the student is female given they are over 1.2m   is  \frac{9}{20}.

14. The Venn diagram below shows information about the number of students who study history and geography.

H = history

G = geography

Work out the probability that a student chosen at random studies only history.

We are told that there are 100 students in total. Therefore:

x = 12 or x = -3 (not valid) If x = 12, then the number of students who study only history is 12, and the number who study only geography is 24. The probability that a student chosen at random studies only history is \frac{12}{100}.

15. 50 people were asked whether they like camping, holiday home or hotel holidays.

18\% of people said they like all three. 7 like camping and holiday homes but not hotels. 11 like camping and hotels. \frac{13}{25} like camping.

Of the 27 who like holiday homes, all but 1 like at least one other type of holiday. 7 people do not like any of these types of holiday.

By representing this information on a Venn diagram, find the probability that a person chosen at random likes hotels given that they like holiday homes.

Put this information onto a Venn diagram.

We are told that the person likes holiday homes. There are 27 people who like holiday homes. 19 of these also like hotels. Therefore, the probability that the person likes hotels given that they like holiday homes is \frac{19}{27}.

Free GCSE maths revision resources for schools As part of the Third Space Learning offer to schools, the personalised online GCSE maths tuition can be supplemented by hundreds of free GCSE maths revision resources from the secondary maths resources library including: – GCSE maths past papers – GCSE maths predicted papers – GCSE maths worksheets – GCSE maths questions – GCSE maths topic list

More KS3 and KS4 maths questions:

• 15 Probability Questions
• 15 Ratio Questions
• 15 Trigonometry Questions
• 15 Algebra Questions
• 15 Simultaneous equations questions
• 15 Pythagoras theorem questions
• Long Division Questions
• Ratio Table Questions

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist GCSE maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn about the GCSE revision programme or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Related articles

15 Pythagoras Theorem Questions And Practice Problems (KS3 & KS4)

Fluent In Five: A Daily Arithmetic Resource For Secondary

15 Simultaneous Equations Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

15 Trigonometry Questions And Practice Problems (KS3 & KS4): Harder GCSE Exam Style Questions Included

FREE GCSE Maths Practice Papers (Edexcel, AQA & OCR)

8 sets of free exam papers written by maths teachers and examiners.

Each set of exam papers contains the three papers that your students will expect to find in their GCSE mathematics exam.

Privacy Overview

Or search by topic

Number and algebra.

• Place value and the number system
• Fractions, decimals, percentages, ratio and proportion
• Calculations and numerical methods
• Algebraic expressions, equations and formulae
• Coordinates, functions and graphs
• Patterns, sequences and structure
• Properties of numbers

Geometry and measure

• 3D geometry, shape and space
• Transformations and constructions
• Vectors and matrices
• Measuring and calculating with units
• Pythagoras and trigonometry
• Angles, polygons, and geometrical proof

Probability and statistics

• Handling, processing and representing data
• Probability (spec_group)

Working mathematically

• Thinking mathematically
• Mathematical mindsets

Advanced mathematics

• Decision mathematics and combinatorics
• Advanced probability and statistics

For younger learners

• Early years foundation stage

Venn diagrams

Take a look at the interactivity below. Before you try anything, have a think about these questions:

What do you see? What do you wonder?

We call this way of sorting information a Venn diagram (named after the mathematician John Venn).

Can you drag the numbers from 1 to 30 into their correct places in the Venn diagram? How do you know where to put each number?

Here is another one for you to try. How do you know where to put each number this time?

If you would prefer to work away from a screen, you could print off these sheets , which have a copy of each Venn diagram on them. 

Here is a screenshot (a picture) of the interactivity, but the labels of the Venn diagram are missing.

What could the labels be?

Here is another version of the interactivity for you to try.

What do you notice this time? Can you explain your 'noticings'?  

If you click on the purple cog of the interactivity, you can change the settings and create your own Venn diagrams for someone else to complete.

Where would you put a number which is a multiple of 5 but not even? Where would an even multiple of 5 go? Where would a number which is odd but not a multiple of 5 go? Where would you put a number which is not a multiple of 5 and not even?

Thank you to everybody who sent in their answers to these questions.

Tetsu from St Michael's International School in Japan sent us some ideas about how a Venn diagram might work. Tetsu noticed that there are two circles that overlap, and the middle part where they overlap is where we write numbers that are both even and are multiples of 5. Well done for writing down what you could see and what you wondered when you looked at the diagram!

Harry from Copthorne Prep School in the UK noticed that only the numbers that met the description of the circle were allowed in. He worked out that if they met the descriptions of both circles then they went into the crossover part, and if they didn't meet the description of either circle then they had to stay outside. He made this video explaining how to put the numbers into the Venn diagrams:

Well done, Harry! We've also uploaded an image of Harry's solutions .

Lyra, Giselle and Taylor from Westridge in the USA explained their ideas for the first three Venn diagrams:

You would put the not even numbers and multiples of 5 in the right circle (multiples of 5), put the both even and multiples of 5 numbers in the middle (where the circles combine), put the even numbers that are not multiples of 5 in the left circle, and you would put the numbers that are neither even or multiples of 5 outside of the circle.

In the second diagram, put the numbers that are less than 20 that are not odd in the right circle, the numbers that are odd and not less than 20 you put in the left circle, put the numbers that are odd and less than 20 in the middle (where the circles combine), and put the numbers that are neither odd or less than 20 outside of the circles.

In the third diagram, the labels should be: the left one should be labeled "odd", and the right one should be labeled "higher than 20".

Thank you all for explaining this so clearly.

Abbie, also from Westridge, noticed something interesting about the last diagram:

Also, for the diagram that says "even numbers" and "odd numbers", there can't be an even AND odd number unless you are going to count zero. That would be a trick question to those who don't know their numbers well enough yet.

That's a really good idea, Abbie - I wonder if we would count zero as even number, an odd number, both or neither!

Haleema from Pierrepont Gamston Primary School also had an idea about the last diagram:

The thing I noticed on the last one was that if the labels are even and odd numbers there can't be anything in the middle. I don't think a Venn diagram should have been used for that. Maybe you could draw circles and label them but there just shouldn't be a middle section.

This is a good idea, Haleema - if we drew a diagram with two circles that didn't overlap, would that still be a Venn diagram or would it be a different type of diagram? I wonder if there are any other types of diagram we could use for two types of numbers where there isn't any overlap.

Finally, Sarah from the ABQ Seeb International School in Oman sent us this video explaining how to put the numbers into the first Venn diagram and into her own Venn diagram:

Thank you for that very clear explanation, Sarah.

Venn Diagrams

Why do this problem.

This problem provides an opportunity for children to become familiar with Venn diagrams, whilst reinforcing knowledge of number properties. Placing numbers in a Venn diagram requires children to consider more than one property of a number at the same time. This problem is also a good context in which to encourage learners to articulate their reasoning.

Possible approach

This activity featured in an  NRICH Primary webinar  in March 2021.

You could introduce the task by projecting the first version of the interactivity using an interactive whiteboard. Without doing anything at all, invite learners to consider what they see and what they wonder.

After giving some time for children to talk in pairs, bring them together to share their thoughts and any questions they have. Through this whole group discussion, you can draw out the features of Venn diagrams and you may like to invite some children to come and drag a number to the correct place, and ask someone else to explain why that is correct. Equally valid is to ask someone to drag a number to an incorrect cell, again asking for an explanation from a different learner.

You can set the children off on the task, either using the interactivity if you have access to tablets/computers, or on paper. This sheet contains copies of the first two diagrams in the problem. If children work in pairs it will encourage them to construct mathematical arguments to convince each other where on the diagram each number belongs. Explaining out loud in this way often helps to clarify thinking and will give a purpose for accurate use of mathematical vocabulary.

You could listen out for misconceptions or disagreements to share in a plenary so that all children become involved in the reasoning. You may also like to look at the image of the diagram with missing labels in the plenary. Give learners time to talk in their pairs before inviting a few to share their solution. You will find that different pairs have 'homed in' on different numbers to help them solve this part of the task, therefore it is worth hearing from a few so that more than one strategy is shared. 

You can end the lesson with the final interactivity. What do they notice? You may need to encourage the class to start dragging numbers into the correct places before they realise that there won't be any numbers in the intersecting region in the middle. Why not?

Clicking on the purple cog of the interactivity allows you to change the settings so you can tailor the labels and sets of numbers to suit your learners.

Key questions

Possible extension.

Children can create their own Venn diagrams for others to complete. Alternatively, you could challenge them to create Venn diagrams which have certain criteria e.g. an empty intersection (like the final example in the problem); all items in the intersection; three overlapping sets etc.

Possible support

Some learners might find it easier to collect numbers with a certain property, for example, even numbers or numbers less than 10, in single circles. Then they can look at those that should go in both circles.

• School Guide
• Mathematics
• Number System and Arithmetic
• Trigonometry
• Probability
• Mensuration
• Maths Formulas
• Class 8 Maths Notes
• Class 9 Maths Notes
• Class 10 Maths Notes
• Class 11 Maths Notes
• Class 12 Maths Notes

Venn Diagram

Venn Diagrams are used for the visual representation of relationships as they provide a clear, visual method for showing how different sets intersect, overlap, or remain distinct. Venn diagrams are essential tools in mathematics and logic for illustrating the relationships between sets. By employing intersecting circles or other shapes, Venn diagrams visually represent how different sets overlap, share common elements, or remain distinct.

They are commonly used to categorize items graphically, underscoring their similarities and distinctions. In this article, we will discuss all the topics related to the Venn diagram, such as Venn Diagram definition, Venn Diagram examples, and various terms related to it.

• What is a Venn Diagram?

Venn Diagrams are used to represent the groups of data in circles, if the circles are overlapping, some elements in the groups are common, if they are not overlapping, there is nothing common between the groups or sets of data.

A Venn diagram is a graphical representation of mathematical or logical relationships between different sets. It consists of overlapping circles, each representing a set, with the overlapping areas illustrating the common elements shared by the sets.

Venn Diagrams are used for Visual Representation of Relationships as they provide a clear, visual method for showing how different sets intersect, overlap, or remain distinct. This helps in understanding complex relationships between sets in mathematics.

In a Venn diagram sets are represented as circles and the circles are shown inside the rectangle which represents the Universal set. A universal set contains all the circles since it has all the elements present involving all the sets.

Table of Content

Venn Diagram Examples

How to draw a venn diagram, venn diagram for sets operations, terms related to venn diagram, venn diagram symbols, types of venn diagrams, venn diagram for three sets, venn diagram formula, uses and applications of venn diagram, solved example problems on venn diagram, venn diagrams practice questions.

Venn diagrams are highly useful in solving problems of sets and other problems. Venn diagrams are useful in representing the data in picture form. Let’s learn more about the Venn diagram through an example,

Example 1: Take a set A representing even numbers up to 10 and another set B representing natural numbers less than 5 then their interaction is represented using the Venn diagram.

The above symbols are used while drawing and showing the relationship among sets. In order to draw a Venn diagram.

Step 1: Start by drawing a Rectangle showing the Universal Set.

Step 2: According to the number of sets given and the relationship between/among them, draw different circles representing different Sets.

Step 3: Find the intersection or union of the set using the condition given.

Read More: Representation of a Set

There are different operations that can be done on sets in order to find the possible unknown parameter, for example, if two sets have something in common, their intersection is possible. The basic operations performed on the set are,

• Union of Set
• Intersection of Set
• Complement of Set
• Difference of Set

Let’s look at these set operations and how they look on the Venn diagram.

Venn Diagram of Union of Sets

The Union of two or more two sets represents the data of the sets without repeating the same data more than once, it is shown with the symbol ⇢∪.

n(A∪ B) = {a: a∈ A OR a∈ B}

Venn Diagram of Intersection of Sets

The intersection of two or more two sets means extracting only the amount of data that is common between/among the sets. The symbol used for the intersection⇢ ∩.

n(A∩ B)= {a: a∈ A and a∈ B}

Venn Diagram of Complement of a Set

Complementing a set means finding the value of the data present in the Universal set other than the data of the set.

n(A’) = U- n(A)

Venn Diagram of Difference of Set

Suppose we take two sets, Set A and Set B then their difference is given as A – B. This difference represents all the values of set A which are not present in set B.

For example, if we take Set A = {1, 2, 3, 4, 5, 6} and set B = {2, 4, 6, 8} then A- B = {1, 3, 5}. 

In the Venn diagram, we represent the A – B as the area of set A which is not intersecting with set B.

The concept of the Venn diagram is very useful for solving a variety of problems in Mathematics and others. To understand more about it lets learn some important terms related to it.

Universal Set

Universal Set is a large set that contains all the sets which we are considering in a particular situation.

For example, suppose we are considering the set of Honda cars in a society say set A, and let set B is the group of red car in the same society then the set of all the cars in that society is the universal set as it contains the values of both the sets , set A and set B in consideration.

The image representing the Universal set is discussed below,

Subset is actually a set of values that is contained inside another set i.e. we can say that set B is the subset of set A if all the values of set B are contained in set A.

For example, if we take N as the set of all the natural numbers and W as the set of all whole numbers then,

• N = Set of all Natural Numbers
• W = Set of all Whole Numbers

We can say that N is a subset of W all the values of set N are contained in set W i.e.,N ⊆ W

We use Venn diagrams to easily represent a subset of a set. The images discussing the subset of a set are given below,

In order to draw a Venn diagram, first, understand the type of symbols used in sets. Sets can be easily represented on the Venn diagram and the parameters are easily taken out from the diagram itself. We use various types of symbols in drawing Venn diagrams, some of the most important types of symbols used in drawing Venn diagrams are,

There are various types of Venn diagrams that are widely used in Mathematics and other related fields. The various types of Venn diagrams are categorized based on the number of sets involved or circles involved in the Universal set.

• Two-set Venn diagram
• Three-set Venn diagram
• Four-set Venn diagram
• Five-set Venn diagram

We can represent three sets easily using the Venn Diagram. Their representation is done by three overlapping circles. Suppose we take three sets of Set A of the people who play cricket. Set B of the people who are graduates and Set C of the people who are 18 years and above of the age. 

Then the Venn diagram representing the above three sets is drawn using three circles and taking their intersection wherever required.

We can represent the intersection of three sets using the Venn diagram. The below image represents the intersection of three sets.

We can find the various parameters using the above Venn diagram.

Suppose we have to find,

• No of graduates who play cricket it is given by B⋂C
• No of graduates who play cricket and are at least 18 years old is given by A⋂B⋂C , etc.

Also Check:

Difference of Sets Universal Set Equal Sets

We use various formulas of the set to find various parameters of the sets. 

Let’s take two sets, set A and set B then the various formulas of the sets are,

n(A U B) = n(A) + n(B) – n (A ⋂ B)

• n(A) represents the number of elements in set A,
• n(B) represents the number of elements in set B,
• n(A U B) represent the number of elements in A U B, and
• n(A ⋂ B)  represent the number of elements in A ⋂ B

Similarly, for three sets, Set A, Set B, and Set C we get,

n (A U B U C) = n(A) + n(B) + n(C) – n(A ⋂ B) – n(B ⋂ C) – n(C ⋂ A) + n(A ⋂ B ⋂ C)

We can understand these formulas with the help of the example discussed below,

Example: In a class of 40 students, 18 like Mathematics, 16 like Science, and 10 like both Mathematics and Science. Then find the students who like either Mathematics or Science.

Let A be the set of students who like Mathematics and B be the set of students who like Science, then n(A) = 18, n(B) = 16, and n(A ⋂ B) = 10 Now to find the number of students who like either Mathematics or Science i.e. n(A U B) we use the above formula. n(A U B) = n(A) + n(B) – n (A ⋂ B) ⇒ n(A U B) = 18 + 16 – 10 ⇒ n(A U B) = 24

Venn diagrams have various use cases such as solving various problems and representing the data in an easy-to-understand format. Various applications of Venn Diagrams are:

• The relation between various sets and their operations can be easily achieved using Venn diagrams.
• Venn diagrams are used for explaining large data sets in a very easy way.
• Venn diagrams are used for logic building and finding the solution to complex data problems.
• Venn diagrams are used to solve problems based on various analogies.
• Analysts use Venn diagrams to represent complex data in easily understandable ways, etc.

Related Article on Venn Diagram:

Operations on Sets Types Of Sets Set Theory Formulas

Example 1: Set A= {1, 2, 3, 4, 5} and U= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

Represent A’ or A c on the Venn diagram.

Venn Diagram for A’

Example 2: In a Group of people, 50 people either speak Hindi or English, 10 prefer speaking both Hindi and English, 20 prefer only English. How many people prefer speaking Hindi? Explain both by formula and by Venn diagram.

According to formula, n(H∪E) = n(H) + n(E) – n(H∩E) Both English and Hindi speakers, n(H∩E) = 10 English speakers, n(E)= 20 Either Hindi or English, n(H∪E)= 50 50= 20+ n(H) – 10 n(H)= 50 – 10 n(H)= 40 From Venn Diagram,

Example 3: In a Class, Students like to play these games- Football, Cricket, and Volleyball. 5 students Play all 3 games, 20 play Football, 30 play Volleyball, and 40 play Cricket. 10 play both cricket and volleyball, 12 play both football and cricket, 9 play both football and volleyball. How many students are present in the class?

n(F∪ C∪ V)= n(F)+ n(C)+ n(V) – n(F∩C) – n(F∩V) – n(C∩V)+ n(F∩ C∩ V) n(F∪ C∪ V)= 20+ 30+ 40- 10-12-9+5 n(F∪ C∪ V)= 64 There are 64 Students in the class.

Example 4: Represent the above information with the help of a Venn diagram showing the amount of data present in each set.

Above information should look something like this on Venn diagram,

Example 5: Below given Venn diagram has all the sufficient information required to show the data of all the sets possible. Observe the diagram carefully then answer the following.

• What is the value of n(A∩ B∩ C)?
• What is the value of n(C)?
• What is the value of n(B ∩ A)?
• What is the value of n(A∪ B∪ C)?
• What is the value of n(B’)?

Observing the Venn diagram, the above questions can be easily answered, 1. n(A ∩ B∩ C)= 5 2. n(C)= 15+ 5+5+5= 30 3. n( B∩A)= 5+5= 10 4. n(A∪ B∪ C)= 15+ 20+ 10+ 5+ 5+ 5+ 5= 65 5. n(B’)= U- n(B)= 100- (20+ 5+ 5+ 5)= 100- 35= 65

Q1. Consider two sets, A and B, where A represents fruits and B represents vegetables. Set A contains apples, bananas, and grapes, while set B contains carrots, lettuce, and apples. Draw a Venn diagram to represent these sets. How many items are only in the fruit category?

Q2. In a small neighborhood, 10 households have dogs, 7 have cats, and 3 households have both dogs and cats. How many households have at least one kind of pet? Draw a Venn diagram to represent this situation.

Q3. In a sports club, 120 members play tennis, 150 play badminton, and 50 play both tennis and badminton. How many members play either tennis or badminton? Create a Venn diagram to help you answer.

Venn diagrams, created by English logician John Venn in the 1880s, visually represent the logical relationships among sets. Using overlapping circles within a rectangle (the universal set), they illustrate how sets intersect, differ, and relate, with each circle representing a different set. Overlapping regions show common elements, while non-overlapping areas highlight unique element. Venn diagrams are applied across various fields for problem-solving, data presentation, and logical reasoning , making them a versatile tool for educators, students, and professionals alike.

Venn Diagrams – FAQs

What is a venn diagram in mathematics.

Venn diagrams are important ways to represent complex logical relations. They were first implemented by the famous mathematician John Venn. They are used to represent the relation between various sets.

How to Read a Venn Diagram?

We can read the Venn diagram with the help of the following steps, Observe all the circles in the entire diagram as they represent various sets of data. Every circle in the diagram represent a particular data set. These circles are overlapped according to various conditions present. Study the circles and their interaction to identify various data in the diagram

What is A ∩ B Venn Diagram?

A ∩ B signifies the common element between set A and set b and it is read as A intersection B. In Venn, diagram set A is represented using a circle and similarly set b is represented using another circle then their intersection A ∩ B is represented by the overlapping of the circle of set A and set B.

What is ∩ in a Venn Diagram?

In a Venn Diagram, the symbol ∩ represents the intersection, which indicates the portion that is common to both sets.

What are Types of Venn Diagram?

Venn diagrams come in various types based on the number of sets they represent. The different types include: Two-set Venn diagram Three-set Venn diagram Four-set Venn diagram Five-set Venn diagram

What is Venn Diagram is Used for?

A Venn diagram is a visual tool used in logic theory and set theory to show the relationship between different sets or data.

How to Use a Venn Diagram?

To use a Venn Diagram follow the steps added below: Step 1: Draw circles to represent each set. Step 2: Label each circle with the name of the set. Step 3: Place common elements in the overlapping areas. Step 4: Place unique elements in the non-overlapping areas.

What are the Parts of a Venn Diagram?

The main parts of a Venn Diagram are: Circles: Representing the sets. Overlapping Areas: Showing common elements. Non-overlapping Areas: Showing unique elements. Universal Set: Often represented by a rectangle surrounding the circles.

What is the Purpose of a Venn Diagram?

The purpose of a Venn Diagram is to visually display the relationships between different sets, making it easier to compare and contrast data, identify similarities and differences, and understand set operations.

What is Intersection in a Venn Diagram?

Intersection in a Venn Diagram is the overlapping area of the circles, showing elements that are common to all the sets involved.

What is Union in a Venn Diagram?

Union in a Venn Diagram includes all elements from all the sets, represented by the entire area covered by the circles.

How can Venn Diagrams Help in Problem-Solving?

Venn Diagrams help in problem-solving by providing a clear visual representation of sets and their relationships, which makes it easier to analyze complex data and find solutions.

What are Some Common Uses of Venn Diagrams?

Common uses of Venn Diagrams include: Comparing and contrasting information. Solving math problems involving sets. Analyzing survey data. Illustrating logical relationships in various fields.

Can Venn Diagrams be used for more than Three Sets?

Yes, Venn Diagrams can be used for more than three sets, but they become more complex and harder to draw. Typically, diagrams with up to three sets are most common and easiest to understand.

How do you Draw a Venn Diagram for Three Sets?

To draw a Venn Diagram for three sets follow the steps added below: Step 1: Draw three overlapping circles. Step 2: Label each circle with the set name. Step 3: Fill in the overlapping areas with common elements. Step 4: Place unique elements in the non-overlapping parts of each circle.

Why are Venn Diagrams Important in Statistics?

Venn Diagrams are important in statistics because they help visualize relationships between different data sets, making it easier to analyze and interpret statistical data.

Please Login to comment...

Similar reads.

• School Learning
• Maths-Class-11

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

VENN DIAGRAM WORD PROBLEMS WITH 3 CIRCLES

Let us consider the three sets A, B and C.

Set A contains a elements, B contains b elements and C contains c elements.

Both A and B contains w elements, B and C contains x elements, A and C contains y elements, all the three sets A, B and C contains z elements.

We can use Venn diagram with 3 circles to represent the above information as shown below. 

Let us do the following changes in the Venn diagram. 

We can get the following results from the Venn diagram shown above.

Number of elements related only to A is 

=  a - (w + y - z)

Number of elements related only to B is 

=  b - (w + x - z)

Number of elements related only to C is 

=  c - (y + x - z)

Number of elements related only to (A and B) is

=  w - z

Number of elements related only to (B and C) is

=  x - z

Number of elements related only to (A and C) is

=  y - z

Number of elements related to all the three sets A, B and C is 

Total number of elements related to all the three sets A, B and C  is

= [a-(w+y-z)] + [b-(w+x-z)] + [c-(y+x-z)] + (w-z) + (x-z) + (y-z) + z 

Example 1 :

In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only.

Let M, C and P represent the courses Mathematics, Chemistry and Physics respectively.

Venn diagram related to the information given in the question: 

From the venn diagram above, we have

No. of students who had taken only math  =  24

No. of students who had taken only chemistry  =  60

No. of students who had taken only physics  =  22

Total no. of students who had taken only one course :

=  24 + 60 + 22

=  106

So, the total number of students who had taken only one course is 106.

Example 2 :

In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group  (Assume that each student in the group plays at least one game.)

Let F, H and C represent the games football, hockey and cricket respectively. 

Venn diagram related to the information given in the question :

Total number of students in the group :

=  28 + 12 + 18 + 7 + 10 + 17 + 8

=  100

So, the total number of students in the group is 100.

Example 3 :

In a college, 60 students enrolled in chemistry,40 in physics, 30 in biology, 15 in chemistry and physics,10 in physics and biology, 5 in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects.

Let C, P and B represent the subjects Chemistry, Physics and Biology respectively.

From the above Venn diagram, number of students enrolled  in at least one of the subjects :

=  40 + 15 + 15 + 15 + 5 + 10 + 0

So, the number of students  enrolled in at least one of the subjects is 100.

Example 4 :

In a town 85% of the people speak Tamil, 40% speak English and 20% speak Hindi. Also 32% speak Tamil and English, 13% speak Tamil and Hindi and 10% speak English and Hindi, find the percentage of people who can speak all the three languages.

Let T, E and H represent the people who speak the languages Tamil, English and Hindi respectively. 

Let x be the percentage of people who speak all the three languages.

From the above Venn diagram, we can have 

100  =  40 + x + 32 – x + x + 13 – x + 10 – x – 2 + x – 3 + x

100  =  40 + 32 + 13 + 10 – 2 – 3 + x 

100  =  95 – 5 + x

100  =  90 + x

x  =  100 - 90

x  =  10% 

So, the percentage of people who speak all the three languages is 10%. 

Example 5 :

An advertising agency finds that, of its 170 clients, 115 use Television, 110 use Radio and 130 use Magazines. Also 85 use Television and Magazines, 75 use Television and Radio, 95 use Radio and Magazines, 70 use all the three. Draw Venn diagram to represent these data. Find 

(i) how many use only Radio?

(ii) how many use only Television?

(iii) how many use Television and Magazine but not radio?

Let T, R and M represent the people who use Television, Radio and Magazines respectively.

From the above Venn diagram, we have

(i) Number of people who use only Radio is 10

(ii) Number of people who use only Television is 25

(iii) Number of people who use Television and Magazine but not radio is 15.

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

• Sat Math Practice
• SAT Math Worksheets
• PEMDAS Rule
• BODMAS rule
• GEMDAS Order of Operations
• Math Calculators
• Transformations of Functions
• Order of rotational symmetry
• Lines of symmetry
• Compound Angles
• Quantitative Aptitude Tricks
• Trigonometric ratio table
• Word Problems
• Times Table Shortcuts
• 10th CBSE solution
• PSAT Math Preparation
• Privacy Policy
• Laws of Exponents

Recent Articles

Digital sat math problems and solutions (part - 28).

Aug 16, 24 10:16 PM

SAT Math Resources (Videos, Concepts, Worksheets and More)

Derivative problems and solutions (part - 7).

Aug 16, 24 05:48 AM