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## 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

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## 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?

## 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)

## 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.

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

Number of elements related only to B is

Number of elements related only to C is

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

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

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

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

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 :

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

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

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

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.

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

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.

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.

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## How to Graph Linear Equations in Slope Intercept Form

## Laws of Exponents Worksheet

Three circle Venn Diagrams are a step up in complexity from two circle diagrams.

A Music Survey was carried out to find out what types of music a group of people liked.

The results were placed into the following three circle Venn Diagram.

The type of three circle Venn Diagram we will need is the following:

We need the exact same type of Venn Diagram as for Question 1.

When we place what we know so far onto the diagram, this is what we have:

We can now fill in the answer of “2” onto the centre of our diagram.

We can now fill in the answer of “1” onto our diagram.

This information refers to the following section of the Venn Diagram.

We can now fill in the answer of “6” onto our diagram.

We can now place the “Cats Only” answer onto our diagram.

We now only need to work out “Dogs Only”.

Our Diagram for Problem Two is now finally complete.

Venn Diagram Word Problems Summary

Here is a great Venn Diagrams video which also explains the “Inclusion / Exclusion” method.

Introduction to Venn Diagrams Venn Diagram Word Problems Real World Venn Diagrams

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## 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

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## Calculating a 3 Circle Venn Diagram only knowing A, B, and C?

If there are 40 students in a class, 30 of them got A in Music, 33 of them got A in PE, and 37 of them got A in Art, at least how many students got all 3 As?

The first thing that came to my mind is to use Venn Diagram to solve it.

But this kind of problem must be able to be "reverse engineered" just like any other math problem.

$A+B+C-A \cap B-A \cap C-B \cap C + A \cap B \cap C =40$ (Assuming that nobody got no As)

$\overline{A}=(B-A \cap B) + (C-A \cap C) - B \cap C=10$

$\overline{B}=(A-A \cap B) + (C-B \cap C) - A \cap C=7$

$\overline{C}=(B-B \cap C) + (A-A \cap C) - A \cap B=3$

So then I thought, maybe I shouldn't assume that nobody got no As.

And set a $\alpha$ as the number of students that got no As.

Could somebody please be so kind and tell me where did I do wrong?

Where there "not necessary" have to have $A \cap B \cap C$ .

Which means this way of calculation is "completely wrong"!

So I thought, maybe I could set it up like

And found out that this linear equation simply "does not have enough information" to go on.

Could somebody please be so kind and teach me the correct way of doing it?

I found out why it's always 0:

- 1 $\begingroup$ Notice that it asks ‘ at least how many got A’s in all 3 subjects?” $\endgroup$ – Bram28 Feb 21, 2022 at 13:59
- $\begingroup$ @Bram28 Please be so kind and take a look at my update. $\endgroup$ – Noob002 Feb 21, 2022 at 14:55

## 2 Answers 2

"Hint: How many total A's were there out of how many total grades?"

- $\begingroup$ Wow! This is much easier to understand! I guess I went on the wrong direction "from the very beginning" because it was so similar to Venn Diagram problems and got mislead by it! Thank you very much for your help! $\endgroup$ – Noob002 Feb 21, 2022 at 19:31
- $\begingroup$ This is more like an "IQ test" than a regular question! ToT $\endgroup$ – Noob002 Feb 21, 2022 at 19:38

Let $x = |A\cap B\cap C|$ be the number of students that got all As.

We use the inclusion-exclusion formula,

$$ |A| + |B| + |C| - |A\cap B| - |B\cap C|-|C\cap A| + |A\cap B\cap C| = |A\cup B\cup C|,$$

$$x = |A\cup B\cup C| - |A| - |B| - |C| + |A\cap B| + |B\cap C|+|C\cap A|$$

Thus $x \geq |A|+|B|+|C| - 2\cdot40 = 20$ , because $40 \geq |A\cup B\cup C|$ .

- $\begingroup$ Okay I might be wrong but I am fairly certain that while this bound is correct it is not tight. I think the correct lower bound is 20. You can see this by first noting that 30 people are in A. Then by assigning as many from B to not be in a we see that the intersection of A and B has at least 23, then applying the same logic with C we get 20. I cannot see any way to only have 17. $\endgroup$ – Fishbane Feb 21, 2022 at 17:12
- $\begingroup$ @Mentastin I think also that 20 is a tight bound. To show that 17 is a tight bound you should show us sets A,B,C where x=17. $\endgroup$ – miracle173 Feb 21, 2022 at 17:14
- $\begingroup$ Yes, that is correct. 20 is the tight bound (the discrepancy is due to first bounding by 37 and then by 40). I will edit. $\endgroup$ – Mentastin Feb 21, 2022 at 17:20
- $\begingroup$ @Mentastin Please rework your proof. But I can't see how you can claim that $|A\cup B\cup C| = 40$ $\endgroup$ – miracle173 Feb 21, 2022 at 17:35
- $\begingroup$ I don't, I claim that $|A\cup B\cup C| \leq 40$. So $x \geq |A|+|B|+|C|-2|A\cup B\cup C| \geq |A|+|B|+|C| -2*40 = 20$. $\endgroup$ – Mentastin Feb 21, 2022 at 17:39

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## Sets Intersection: Intersection Of Three Sets

Related Pages Intersection Of Two Sets Venn Diagrams More Lessons On Sets

## Venn Diagrams Of Three Sets

For the Venn diagram: Step 1: Draw three overlapping circles to represent the three sets.

Step 2: Write down the elements in the intersection X ∩ Y ∩ Z.

Step 3: Write down the remaining elements in the intersections: X ∩ Y, Y ∩ Z and X ∩ Z.

## How To Shade Regions Of Venn Diagrams Involving Three Sets

Example: Shade the indicated region:

Example: Shade the indicated region: 3) (A ∪ B)' ∩ C 4) (A' ∩ B') ∩ C'

## How To Solve Word Problems With 3-Set Venn Diagrams?

- How many signed up only for a math class?
- How many signed up only for an English class?
- How many signed up for math or English?
- How many signed up for neither math nor English?

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## 3 Circle Venn Diagram Worksheets

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## 3 Circle Venn Diagram

What is a 3 circle venn diagram.

A 3 Circle Venn diagram is a way of classifying groups of objects with the same properties.

It has three circles that intersect each other.

The diagram below shows you how a venn diagram with 3 circles works.

## Venn Diagram Worksheets

Need to practice using venn diagrams?

Then this page should hopefully be what you are looking for!

The worksheets on this page have been split into 2 sections:

Each sheet consists of sorting either a table of facts, shapes or numbers.

Each sheet contains one set of objects and a 3 circle venn diagram to sort the objects with.

There is a progression from easier to harder sheets within each section.

Using the sheets in this section will help your child to:

- practice using three circle venn diagrams;
- converting data from a table to a venn diagram;
- practice classifying a range of objects using different properties;
- classifying numbers using properties such as prime, multiples and factors.

## Help using 3 Circle Venn Diagrams

Looking for some help using 3 circle venn diagrams?

This short video will hopefully show you all you need to master them!

## 3rd Grade Venn Digrams

- Venn Diagram 3 Circles Sheet 3:1
- PDF version
- Venn Diagram 3 Circles Sheet 3:2
- Venn Diagram 3 Circles Sheet 3:3
- Venn Diagram 3 Circles Sheet 3:4

## 4th Grade Venn Digrams

- Venn Diagram 3 Circles Sheet 4:1
- Venn Diagram 3 Circles Sheet 4:2
- Venn Diagram 3 Circles Sheet 4:3
- Venn Diagram 3 Circles Sheet 4:4

## Looking for help with venn diagrams?

There is a video to watch with some simple examples worked through.

## Looking for some 2 Circle Venn Diagram Worksheets?

## Inequalities, Multiples and Factors Worksheets

## Third Grade Bar Graph Worksheets

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## 3-circle Venn diagram

- Elements in A and B = elements in A and B only plus elements in A, B, and C.
- Elements in B and C = elements in B and C only plus elements in A, B, and C.
- Elements in A and C = elements in A and C only plus elements in A, B, and C.

## Example showing how to create a 3-circle Venn diagram

Factors of 30 : 1, 2, 3, 5, 6, 10, 15, 30

Factors of 40 : 1, 2, 4, 5, 8, 10, 20, 40

Factors of 100 : 1, 2, 4, 5, 10, 20, 25, 50, 100

## Now take this quiz about 3-circle venn diagram

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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 ...

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

Using Venn Diagrams to Solve Survey Problems · Problem Solving of Sets with 3 circles of Venn Diagram · Venn Diagrams and Sets 07 · Venn Diagrams

In this video we go over a basic word problem involving three sets. We use a venn diagram to answer the series of questions.

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

This three circle word problem is an easy one. All of the number values for each section of the diagram have been given to us in the question.

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 =

But most of the time when we solve Venn Diagram problems, A∩B,A∩C,B∩C, and A∩B∩C are provided, namely, calculate the "total" amount of

The intersection of three sets X, Y and Z is the set of elements that are common to sets X, Y and Z. It is denoted by X ∩ Y ∩ Z.

For 3 variables, first draw 3 circles like this: Now fill in the data given. The total region covered by the 3 circles is 81%, so outside region is 100-81

A 3 Circle Venn diagram is a way of classifying groups of objects with the same properties. It has three circles that intersect each other. Each circle has its

A 3-circle Venn diagram, named after the English logician Robert Venn, is a diagram that shows how the elements of three sets are related using three