solving venn diagram problems

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How to Create a Venn Diagram in Microsoft PowerPoint

Marshall is a writer with experience in the data storage industry. He worked at Synology, and most recently as CMO and technical staff writer at StorageReview. He's currently an API/Software Technical Writer based in Tokyo, Japan, runs VGKAMI and ITEnterpriser, and spends what little free time he has learning Japanese. Read more...

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 customize to fit your needs.

Insert a Venn Diagram

Open PowerPoint and navigate to the “Insert” tab. Here, click “SmartArt” in the “Illustrations” group.

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

Next, choose “Basic Venn” from the group of options that appear. Once selected, a preview and a description of the graphic will appear in the right-hand pane. Select the “OK” button to insert the graphic.

Once inserted, you can customize the Venn diagram.

Customize Your Venn Diagram

There are different ways you can customize your Venn diagram. For starters, you probably want to adjust the size . To do so, click and drag the corner of the SmartArt box. You can also resize individual circles within the diagram by selecting the circle and dragging the corner of its box.

Once resized, you can edit the text in each circle by clicking the circle and typing in the text box. Alternatively, you can click the arrow that appears at the left of the SmartArt box and then enter your text in each bullet.

To add additional circles to the diagram, just click “Enter” in the content box to add another bullet point. Similarly, removing a bullet point will remove that circle from the diagram.

To add text where the circles overlap, you’ll need to manually add a text box and enter text. To add a text box, select “Text Box” in the “Text” group of the “Insert” tab.

You’ll now notice your cursor changes to a down arrow. Click and drag to draw your text box, and then enter text.

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

PowerPoint also offers a few color variations for the SmartArt graphic. Select the SmartArt and then click the “Design” tab that appears. Here, choose “Change Colors” in the “SmartArt Styles” group.

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

You can also change the color of individual circles by right-clicking the border of the circle and selecting “Format Shape” from the context menu.

The “Format Shape” pane will appear in the right-hand side of the window. In the “Shape Options” tab, click “Fill” to display its options, click the box next to “Color,” then select your color from the palette.

Repeat this process for each circle in the diagram until you’re satisfied with the color scheme of your Venn diagram.

Assigning different colors to each circle in the diagram can make the relationship between subjects more distinct.

Venn Diagrams to Plan Essays and More

A Venn diagram is a great tool for brainstorming and creating a comparison between two or more objects, events, or people. You can use this as a first step to creating an outline for a compare and contrast essay .

Simply draw two (or three) large circles and give each circle a title, reflecting each object, trait, or person you are comparing.

Inside the intersection of the two circles (overlapping area), write all the traits that the objects have in common. You will refer to these traits when you compare similar characteristics.

In the areas outside the overlapping section, you will write all of the traits that are specific to that particular object or person.

Creating an Outline for Your Essay Using a Venn Diagram

From the Venn diagram above, you can create an easy outline for your paper. Here is the beginning of an essay outline:

1. Both dogs and cats make great pets.

2. Both have drawbacks, as well.

3. Cats can be easier to care for.

Leaving for a day

4. Dogs can be better companions.

As you can see, outlining is much easier when you have a visual aid to help you with the brainstorming process.

More Uses for Venn Diagrams

Besides its usefulness for planning essays, Venn Diagrams can be used for thinking through many other problems both at school and at home. For example:

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Venn Diagram Examples, Problems and Solutions

On this page:

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:

The following Venn diagram represents the data above:

Now, we are going to answer our questions:

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:

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

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.

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.

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Well explained I hope more on this one

Venn Diagram Word Problems

In these lessons, we will learn how to solve word problems using Venn Diagrams that involve two sets or three sets. Examples and step-by-step solutions are included in the video lessons.

What Are Venn Diagrams?

Venn diagrams are the principal way of showing sets in a diagrammatic form. The method consists primarily of entering the elements of a set into a circle or ovals.

Before we look at word problems, see the following diagrams to recall how to use Venn Diagrams to represent Union, Intersection and Complement.

How To Solve Problems Using Venn Diagrams?

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

Problem 1: 150 college freshmen were interviewed. 85 were registered for a Math class, 70 were registered for an English class, 50 were registered for both Math and English.

a) How many signed up only for a Math Class? b) How many signed up only for an English Class? c) How many signed up for Math or English? d) How many signed up neither for Math nor English?

Problem 2: 100 students were interviewed. 28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects.

a) How many students took none of the three subjects? b) How many students took PE but not BIO or ENG? c) How many students took BIO and PE but not ENG?

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

Problem: At a breakfast buffet, 93 people chose coffee and 47 people chose juice. 25 people chose both coffee and juice. If each person chose at least one of these beverages, how many people visited the buffet?

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

Problem: In a class of 30 students, 19 are studying French, 12 are studying Spanish and 7 are studying both French and Spanish. How many students are not taking any foreign languages?

Probability, Venn Diagrams And Conditional Probability

This video shows how to construct a simple Venn diagram and then calculate a simple conditional probability.

Problem: In a class, P(male)= 0.3, P(brown hair) = 0.5, P (male and brown hair) = 0.2 Find (i) P(female) (ii) P(male| brown hair) (iii) P(female| not brown hair)

Venn Diagrams With Three Categories

Example: A group of 62 students were surveyed, and it was found that each of the students surveyed liked at least one of the following three fruits: apricots, bananas, and cantaloupes.

34 liked apricots. 30 liked bananas. 33 liked cantaloupes. 11 liked apricots and bananas. 15 liked bananas and cantaloupes. 17 liked apricots and cantaloupes. 19 liked exactly two of the following fruits: apricots, bananas, and cantaloupes.

a. How many students liked apricots, but not bananas or cantaloupes? b. How many students liked cantaloupes, but not bananas or apricots? c. How many students liked all of the following three fruits: apricots, bananas, and cantaloupes? d. How many students liked apricots and cantaloupes, but not bananas?

Venn Diagram Word Problem

Here is an example on how to solve a Venn diagram word problem that involves three intersecting sets.

Problem: 90 students went to a school carnival. 3 had a hamburger, soft drink and ice-cream. 24 had hamburgers. 5 had a hamburger and a soft drink. 33 had soft drinks. 10 had a soft drink and ice-cream. 38 had ice-cream. 8 had a hamburger and ice-cream. How many had nothing? (Errata in video: 90 - (14 + 2 + 3 + 5 + 21 + 7 + 23) = 90 - 75 = 15)

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.

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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

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.

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

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.

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.

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:

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

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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.

venn diagram to compare and contrast dogs and cats

The Venn diagram shows the following information:

Both dogs and cats:

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.

example of a venn diagram with 3 circles

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

Only birds:

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

Make a Venn Diagram for the following situation:

30 students were asked which sports they play.

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.

step 1 of making a venn diagram with 3 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.

step 2 of making a venn diagram with 3 circles

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.

step 3 of making a venn diagram with 3 sets

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.

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.

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 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

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

shading AnC on a venn diagram with 3 circles

Shaded Region: A∪B∪C

Shaded Region: A∩B∩C

Shaded Region: (A∩B)∪(A∩C)

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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.

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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%

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:

In addition:

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

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15 Venn Diagram Questions And Practice Problems (Middle School & High School): 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 elementary school and their complexity and uses progress through middle and high school.

This article will look at the types of Venn diagram questions that might be encountered at middle school and high school, with a focus on exam style example questions and preparing for standardized tests. We will also cover problem-solving questions. Each question is followed by a worked solution.

How to solve Venn diagram questions

Venn diagram questions 6th grade, venn diagram questions 7th grade, venn diagram questions 8th grade, lower ability venn diagram questions, middle ability high school venn diagram questions.

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

In middle school, sets and set notation are introduced when working with Venn diagrams. A set is a collection of objects. We identify a set using braces. For example, if set 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 A= factors of 10

Set B= even numbers

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

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.

For Venn diagrams we can say

Middle School Venn diagram questions

In middle school, 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 6th, 7th and 8th grade.

A question on Venn diagrams from third space learning online tutoring

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

15 Venn Diagram Questions Blog Question 1

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?

15 Venn Diagram Questions Question 2 Image 1

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.

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.

Venn Diagram Symbols GCSE Question 3 Option A

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 A and set B . On which Venn diagram has A ′ been shaded?

15 Venn Diagram Questions Question 4 Option A

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

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

15 Venn Diagram Questions Question 5 Image 1

\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.

15 Venn Diagram Questions Question 6 Image 1

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.

15 Venn Diagram Questions Question 6 Image 2

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 theater. 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+\$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 high school, 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 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.

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

15 Venn Diagram Questions Question 8 Image 1

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.

15 Venn Diagram Questions Question 9 Image 1

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

15 Venn Diagram Questions Question 9 Image 2

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}).

15 Venn Diagram Questions Question 10 Image 1

\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.

15 Venn Diagram Questions Question 11 Image 1

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

15 Venn Diagram Questions Question 11 Image 2

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

15 Venn Diagram Questions Question 11 Image 3

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

15 Venn Diagram Questions Question 11 Image 4

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\}.

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.

15 Venn Diagram Questions Question 12 Image 1

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.

15 Venn Diagram Questions Question 12 Image 2

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

15 Venn Diagram Questions Question 13 Image 1

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

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}.

15 Venn Diagram Questions Question 13 Image 2

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.

15 Venn Diagram Questions Question 15 Image 1

Put this information onto a Venn diagram.

15 Venn Diagram Questions Question 15 Image 2

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}.

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The content in this article was originally written by secondary teacher Beki Christian and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.

Individual packs for Kindergarten to Grade 5 containing fun math games and activities to complete independently or with a partner.

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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.

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?

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WORD PROBLEMS ON SETS AND VENN DIAGRAMS

Basic stuff.

To understand, how to solve Venn diagram word problems with 3 circles, we have to know the following basic stuff.

u ----> union (or)

n ----> intersection (and)

Addition Theorem on Sets

Theorem 1 :

n(AuB) = n(A) + n(B) - n(AnB)

Theorem 2 :

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

Explanation :

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

n(AnB) - n(AnBnC) :

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

Total number of elements related to both B & C

n(BnC) - n(AnBnC) :

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

Total number of elements related to both A & C

n(AnC) - n(AnBnC) :

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

For two events A & B, we have

n(A) - n(AnB) :

n(B) - n(AnB) :

Practice Problems

Problem 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, P represent sets of students who had taken mathematics, chemistry and physics respectively.

From the given information, we have

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

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

n(MnCnP) = 14

From the basic stuff, we have

Number of students who had taken only Math

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

= 64 - [28 + 26 - 14]

Number of students who had taken only Chemistry :

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

= 94 - [26+22-14]

Number of students who had taken only Physics :

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

= 58 - [28 + 22 - 14]

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

= 24 + 60 + 22

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

Alternative Method (Using venn diagram) :

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 :

Problem 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 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

n(FnHnC) = 8

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

n(FuHuC) is equal to

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

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

n(FuHuC) = 100

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

Alternative Method (Using Venn diagram) :

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.

Problem 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 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 :

n(CnP) = 15

Number of students enrolled in Physics and Biology :

n(PnB) = 10

Number of students enrolled in Biology and Chemistry :

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

n(CnPnB) = 0

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.

Problem 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 Tamil, English and Hindi respectively.

Percentage of people who speak Tamil :

Percentage of people who speak English :

Percentage of people who speak Hindi :

n(H) = 20

Percentage of people who speak English and Tamil :

n(TnE) = 32

Percentage of people who speak Tamil and Hindi :

n(TnH) = 13

Percentage of people who speak English and Hindi :

n(EnH) = 10

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%.

Problem 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.

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

n (TnM) = 85

Number of people who use Television and Radio :

n(TnR) = 75

Number of people who use Radio and Magazine :

n(RnM) = 95

Number of people who use all the three :

n(TnRnM) = 70

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.

Problem 6 :

In a class of 60 students, 40 students like math, 36 like science, 24 like both the subjects. Find the number of students who like

(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

Answer (i) :

Number of students who like math only :

= n(M) - n(MnS)

Answer (ii) :

Number of students who like science only :

= n(S) - n(MnS)

= 12

Answer (iii) :

Number of students who like either math or science :

= n(M or S)

= n(MuS)

= n(M) + n(S) - n(MnS)

= 40 + 36 - 24

Answer (iv) :

Total n umber students who like Math or Science subjects :

n(MuS) = 52

Number of students who like neither math nor science

Problem 7 :

At a certain conference of 100 people there are 29 Indian women and 23 Indian men. Out of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. Find the number of women doctors attending the conference.

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

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

n(MuD) = n(M) + n(D) - n(MnD)

24 = 23 + 4 - n(MnD)

n(MnD) = 3

n(Indian Men and Doctors) = 3

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.

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Venn Diagram : Basic Concept with Solved Problem
The Venn Diagram Pt.1#mathantics

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What Are the Six Steps of Problem Solving?
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...
How to Create a Venn Diagram in Microsoft PowerPoint
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...
Using a Venn Diagram for a Compare and Contrast Essay
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 ...
Solving Problems with Venn Diagrams
This video solves two problems using Venn Diagrams. One with two sets and one with three sets. Complete Video List at
Problem Solving with Venn diagrams
Solve worded problems using Venn diagrams.
Venn Diagram Examples: Problems, Solutions, Formula Explanation
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 =
Venn Diagram Word Problems
Problem: 90 students went to a school carnival. 3 had a hamburger, soft drink and ice-cream. 24 had hamburgers. 5 had a hamburger
Venn Diagram
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
How to Solve Venn Diagrams 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
Venn Diagrams: Exercises
Venn diagram word problems generally give you two or three
15 Venn Diagram Questions And Practice Problems With Solutions
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
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
Word Problems on Sets and Venn Diagrams
To understand, how to solve Venn diagram word problems with 3 circles, we have to know the following basic stuff. u ----> union (or).
Use Venn diagrams to solve problems
3 students like to watch both soccer and figure skating. Put 3 dots in the area that is in both circles.