Venn Diagram of Make America Great Again

The best fashion to explicate how the Venn diagram works and what its formulas bear witness is to give 2 or 3 circles Venn diagram examples and problems with solutions.

Trouble-solving using Venn diagram is a widely used approach in many areas such as statistics, information scientific discipline, business concern, set theory, math, logic and etc.

On this folio:

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

Let'southward 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 bear witness how given items are similar and dissimilar.

Despite Venn diagram with 2 or 3 circles are the most common type, in that location are as well many diagrams with a larger number of circles (5,six,7,8,10…). Theoretically, they can accept unlimited circles.

Venn Diagram General Formula

n(A ∪ B) = n(A) + due north(B) – northward(A ∩ B)

Don't worry, there is no need to remember this formula, one time you grasp the significant. Let's see the explanation with an example.

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

Where:

10 – the number of items that belong to set A
Y – the number of items that vest to ready B
Z – the number of items that belong to ready A and B both

From the above Venn diagram, it is quite clear that

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

Now, allow'southward movement forrad and think almost Venn Diagrams with iii circles.

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

n(A ∪ B ∪ C) = north(A) + n(B) + north(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 applied examples (bug with solutions) from the real life.

2 Circumvolve Venn Diagram Examples (discussion bug):

Suppose that in a town, 800 people are selected by random types of sampling methods. 280 go to piece of work by car simply, 220 go to piece of work past bicycle merely and 140 employ both ways – sometimes get with a car and sometimes with a bicycle.

Here are some of import questions we will find the answers:

• How many people go to work by car just?
• How many people become to work past bicycle only?
• How many people get by neither car nor wheel?
• How many people use at least ane of both transportation types?
• How many people use only one of car or bicycle?

The following Venn diagram represents the data above:

Now, nosotros 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 ane of both transportation types = n(merely car) + n(only wheel) + north(both car and bicycle) = 280 + 220 + 140 = 640
• Number of people who apply merely ane of car or bicycle = 280 + 220 = 500

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

We volition deep further with a more complicated triple Venn diagram instance.

iii Circle Venn Diagram Examples:

For the purposes of a marketing research, a survey of g 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.

Hither are our questions we should detect the answer:

• How many women like watching all the iii moving picture genres?
• Find the number of women who similar watching only one of the iii genres.
• Discover the number of women who similar watching at least two of the given genres.

Permit's stand for the data in a higher place in a more digestible way using the Venn diagram formula elements:

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

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

94% = 52% + 45% + lx% – 25% – 28% – thirty% + due north (C ∩ F ∩ R)

Solving this uncomplicated math equation, pb us to:

northward (C ∩ F ∩ R) = 20%

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

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

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

• The number of women who like watching all the three genres = 20% of 1000 = 200.
• Number of women who similar watching only one of the three genres = (17% + 12% + 22%) of 1000 = 510
• The number of women who similar watching at least two of the given genres = (number of women who like watching simply 2 of the genres) +(number of women who like watching all the three genres) = (x + 5 + eight + 20)% i.e. 43% of chiliad = 430.

As we mentioned above 2 and 3 circle diagrams are much more than common for problem-solving in many areas such as concern, statistics, information science and etc. Withal, iv circumvolve Venn diagram also has its identify.

4 Circles Venn Diagram Case:

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

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

Hither is the list of the results:

Sport	Name
Football	Robert, James, John, Mary, Jennifer, William
Hockey	Robert, William, Linda, Elizabeth, James
Basketball	William, Jayne, Linda, Daniel, Mary
Netball	Jessica, William, Linda, Elizabeth, Anthony, Mary
None	Dorothy

The side by side step is to draw a Venn diagram to show the information sets nosotros have.

It is very articulate 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 to a higher place Venn diagram examples, it is obvious that this graphical tool tin can aid yous a lot in representing a variety of data sets. Venn diagram likewise is amidst the nigh popular types of graphs for identifying similarities and differences.

Compare and Dissimilarity 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, specially when yous have the right tool. Nowadays, one of the most popular manner to create them is with the assist of paid or complimentary graphing software tools such as:

• Lucidchard
• Canva
• Gliffy

You can employ Microsoft products such equally:

• Word
• Excel
• PowerPoint

Some gratuitous mind mapping tools are besides a good solution. Finally, you tin simply use a sheet of paper or a whiteboard.

Determination:

The to a higher place 2, 3 and 4 circumvolve Venn diagram examples aim to brand y'all empathize better the whole idea behind this diagrams.

As y'all see, the Venn diagram formula tin help you to find solutions for a multifariousness of problems and questions from the real life.

A Venn diagram is a simple but powerful way to represent the relationships betwixt datasets. Information technology 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 information technology data scientific discipline or real-world situations, Venn diagrams are a slap-up weapon in your hand to deal with almost any kind of information.

If you need more than chart examples, our posts fishbone diagram examples and what does scatter plot bear witness might be of assist.

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Source: https://www.intellspot.com/venn-diagram-examples/

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