- Buying Guides

## Complete Guides by How-To Geek

Join 425,000 subscribers and get a daily digest of news, geek trivia, and our feature articles.

By submitting your email, you agree to the Terms of Use and Privacy Policy .

## How to Create a Venn Diagram in Microsoft PowerPoint

## Insert a Venn Diagram

The “Choose A SmartArt Graphic” window will appear. In the left-hand pane, select “Relationship.”

Once inserted, you can customize the Venn diagram.

RELATED: How to Insert a Picture or Other Object in Microsoft Office

## Customize Your Venn Diagram

Repeat this step until you’ve added all the text required for your Venn diagram.

Select the color scheme you like from the drop-down menu that appears.

RELATED: How to Create a Timeline in Microsoft PowerPoint

- › How to Create and Insert a Pyramid in Microsoft PowerPoint
- › How to Create a Venn Diagram in Google Slides
- › How to Animate Parts of a Chart in Microsoft PowerPoint
- › How to Make a Venn Diagram in Google Docs
- › 10 Reasons DVD Movies Are Still Worth Collecting
- › How to Find Favorites on TikTok
- › How to Fix the Attachments Not Showing in Outlook Issue
- › What Is Apple’s Freeform App and How Do You Use It?

## Venn Diagrams to Plan Essays and More

## Creating an Outline for Your Essay Using a Venn Diagram

1. Both dogs and cats make great pets.

- Both animals can be very entertaining
- Each is loving in its own way
- Each can live inside or outside the house

2. Both have drawbacks, as well.

3. Cats can be easier to care for.

4. Dogs can be better companions.

## More Uses for Venn Diagrams

- Planning a Budget: Create three circles for What I Want, What I Need, and What I Can Afford.
- Setting Priorities: Create circles for different types of priorities: School, Chores, Friends, TV, along with a circle for What I Have Time for This Week.
- Choosing Activities: Create circles for different types of activities: What I'm Committed to, What I'd Like to Try, and What I Have Time for Each Week.
- Comparing People's Qualities: Create circles for the different qualities you're comparing (ethical, friendly, good looking, wealthy, etc.), and then add names to each circle. Which overlap?

## Venn Diagram Examples, Problems and Solutions

- 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.

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

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

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)

2 Circle Venn Diagram Examples (word problems):

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

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

3 Circle Venn Diagram Examples:

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:

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.

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.

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

You can use Microsoft products such as:

## About The Author

## Silvia Valcheva

## One Response

Well explained I hope more on this one

## Leave a Reply Cancel Reply

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

## Venn Diagram Word Problems

## What Are Venn Diagrams?

## How To Solve Problems Using Venn Diagrams?

This video solves two problems using Venn Diagrams. One with two sets and one with three sets.

## How And When To Use Venn Diagrams To Solve Word Problems?

## How To Use Venn Diagrams To Help Solve Counting Word Problems?

## Probability, Venn Diagrams And Conditional Probability

## Venn Diagrams With Three Categories

## Venn Diagram Word Problem

## Venn Diagrams With Two Categories

This video introduces 2-circle Venn diagrams, and using subtraction as a counting technique.

## How To Use 3-Circle Venn Diagrams As A Counting Technique?

Learn about Venn diagrams with two subsets using regions.

## Learning Home

## Not Now! Will rate later

## Venn Diagram: Concept and Solved Questions

## What is a Venn Diagram?

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

## Venn Diagram in case of two elements

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

## 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

- 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?

- 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

- 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.

- 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:

## 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.

- 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

Get More Out of Your Exam Preparation - Try Our App!

## How to Solve Venn Diagrams with 3 Circles

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

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

The Venn diagram shows the following information:

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

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.

## 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

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

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.

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

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

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

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

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.

## How to Solve a Venn Diagram with 3 Circles

100 people were asked which pets they have.

- 32 people in total just have a cat
- 18 people in total just have a rabbit
- 10 people have a dog and a rabbit
- 21 people have a dog and a cat
- 7 people have 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

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

10 people have a dog and a rabbit.

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

21 people have a dog and a cat.

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

7 people have 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 just 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 just 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

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

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)

## 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

## 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?

## MathHelp.com

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

(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:

- 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?

Three geckoes were tailless and chewed on but not gray.

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

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

## Standardized Test Prep

College math, homeschool math, share this page.

## Visit Our Profiles

Math teaching support you can trust

## [FREE] Fun Math Games and Activities Packs for Kindergarten to Grade 5

Ready to go, printable packs that teachers can use in the classroom.

## 15 Venn Diagram Questions And Practice Problems (Middle School & High School): Exam Style Questions Included

## Beki Christian

## How to solve Venn diagram questions

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.

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

ξ represents the whole set, called the universal set.

∅ represents the empty set, a set containing no elements.

Let’s check out some other set notation examples!

In middle school and high school, we often use Venn diagrams to establish probabilities.

We do this by reading information from the Venn diagram and applying the following formula.

## Middle School Venn diagram questions

How many people have brown hair and glasses?

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

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

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

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

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

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

\$64+\$48=\$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.

## High school Venn diagram questions

In advanced math classes, Venn diagrams are used to calculate conditional probability.

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.

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

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

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

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

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

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\}

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\}.

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

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

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

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

Put this information onto a Venn diagram.

## Looking for more math questions for middle and high school students ?

- 15 Probability Questions
- 15 Ratio Questions
- 15 Trigonometry Problems
- 15 Algebra Questions
- 15 Simultaneous Equations Questions
- Long Division Problems

The activities are designed to be fun, flexible and suitable for a range of abilities.

## Privacy Overview

## Venn Diagram Questions

## Venn Diagram Questions with Solution

Let us practice some questions based on Venn diagrams.

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.

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)

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

∴ 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.

Let, M ≡ Set of students who chose mathematics

B ≡ Set of students who chose biology

Question 6: Represent The following as Venn diagram:

(i) students who play only outdoor games

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

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

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

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

(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

(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:

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

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?

## Register with BYJU'S & Download Free PDFs

## WORD PROBLEMS ON SETS AND VENN DIAGRAMS

## Addition Theorem on Sets

=n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)

Let us come to know about the following terms in details.

n(AuB) = Total number of elements related to any of the two events A & B.

n(AuBuC) = Total number of elements related to any of the three events A, B & C.

n(A) = Total number of elements related to A

n(B) = Total number of elements related to B

n(C) = Total number of elements related to C

For three events A, B & C, we have

n(A) - [n(AnB) + n(AnC) - n(AnBnC)] :

Total number of elements related to A only

n(B) - [n(AnB) + n(BnC) - n(AnBnC)] :

Total number of elements related to B only

n(C) - [n(BnC) + n(AnC) + n(AnBnC)] :

Total number of elements related to C only

Total number of elements related to both A & B

Total number of elements related to both (A & B) only

Total number of elements related to both B & C

Total number of elements related to both (B & C) only

Total number of elements related to both A & C

Total number of elements related to both (A & C) only

## Practice Problems

From the given information, we have

n(M) = 64, n(C) = 94, n(P) = 58,

n(MnP) = 28, n(MnC) = 26, n(CnP) = 22

Number of students who had taken only Math

= n(M) - [n(MnP) + n(MnC) - n(MnCnP)]

Number of students who had taken only Chemistry :

= n(C) - [n(MnC) + n(CnP) - n(MnCnP)]

Number of students who had taken only Physics :

= n(P) - [n(MnP) + n(CnP) - n(MnCnP)]

Total n umber of students who had taken only one course :

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

Alternative Method (Using venn diagram) :

Venn diagram related to the information given in the question:

From the venn diagram above, we have

Number of students who had taken only math = 24

Number of students who had taken only chemistry = 60

Number of students who had taken only physics = 22

Total Number of students who had taken only one course :

Let F, H and C represent the set of students who play foot ball, hockey and cricket respectively.

n(F) = 65, n(H) = 45, n(C) = 42,

n(FnH) = 20, n(FnC) = 25, n(HnC) = 15

Total number of students in the group is n(FuHuC).

= n(F) + n(H) + n(C) - n(FnH) - n(FnC) - n(HnC) + n(FnHnC)

n(FuHuC) = 65 + 45 + 42 -20 - 25 - 15 + 8

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

Alternative Method (Using Venn diagram) :

Venn diagram related to the information given in the question :

Total number of students in the group :

= 28 + 12 + 18 + 7 + 10 + 17 + 8

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

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

Number of students enrolled in Chemistry :

Number of students enrolled in Physics :

Number of students enrolled in Biology :

Number of students enrolled in Chemistry and Physics :

Number of students enrolled in Physics and Biology :

Number of students enrolled in Biology and Chemistry :

No one enrolled in all the three. So, we have

The above information can be put in a Venn diagram as shown below.

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.

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

Percentage of people who speak Tamil :

Percentage of people who speak English :

Percentage of people who speak Hindi :

Percentage of people who speak English and Tamil :

Percentage of people who speak Tamil and Hindi :

Percentage of people who speak English and Hindi :

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

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

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

(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.

Number of people who use Television :

Number of people who use Radio :

Number of people who use Magazine :

Number of people who use Television and Magazines

Number of people who use Television and Radio :

Number of people who use Radio and Magazine :

Number of people who use all the three :

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.

(i) Math only, (ii) Science only (iii) Either Math or Science (iv) Neither Math nor science.

Let M and S represent the set of students who like math and science respectively.

From the information given in the question, we have

n(M) = 40, n(S) = 36, n(MnS) = 24

Number of students who like math only :

Number of students who like science only :

Number of students who like either math or science :

Total n umber students who like Math or Science subjects :

Number of students who like neither math nor science

Let M and D represent the set of Indian men and Doctors respectively.

n(M) = 23, n(D) = 4, n(MuD) = 24

So, out of the 4 Indian doctors, there are 3 men.

And the remaining 1 is Indian women doctor.

So, the number women doctors attending the conference is 1.

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

Graphing linear equations in slope intercept form worksheet.

## IMAGES

## VIDEO

## COMMENTS

The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

One of Microsoft PowerPoint’s charms is the ability to convey messages through illustrations, images, and SmartArt graphics. In its library of SmartArt graphics, PowerPoint provides a Venn diagram template, which you can completely customiz...

The Venn diagram is a great tool for brainstorming and creating a comparison between two or more objects, events, or people. A Venn diagram is a great tool for brainstorming and creating a comparison between two or more objects, events, or ...

This video solves two problems using Venn Diagrams. One with two sets and one with three sets. Complete Video List at

Solve worded problems using Venn diagrams.

Venn Diagram Examples, Problems and Solutions · n(C) = percentage of women who like watching comedy = 52% · n(F) = percentage of women who like watching fantasy =

Problem: 90 students went to a school carnival. 3 had a hamburger, soft drink and ice-cream. 24 had hamburgers. 5 had a hamburger

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

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

Venn diagram word problems generally give you two or three

Venn diagrams sort objects, called elements, into two or more sets. ... {1,2,3,4,5,6,7,8,9,10} sorted into the following

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

To understand, how to solve Venn diagram word problems with 3 circles, we have to know the following basic stuff. u ----> union (or).

3 students like to watch both soccer and figure skating. Put 3 dots in the area that is in both circles.