: Intersection between two sets.It shows what items are shared between categories.

An ac component of a set.Any item that is not represented in the set is the complement.


Let's talk serious Venn diagrams-and not the kind you remember from grade school.The goal is to represent complex mathematical ideas through hardcore visuals produced by professionals.

In a branch of logic called set theory, Venn diagrams represent collections of mathematical sets - that is, mathematical collections of objects.Our modern understanding of infinity and real numbers was developed through the set theory, one of the foundations of mathematics.

To understand set theory, researchers and mathematicians have developed a language and notation system.You will need to become familiar with these Venn diagram symbols if you want to know their secrets.

As you progress through the process of making a Venn diagram, you will learn about the symbols.huckleberrypersimmon.com will be used for our examples because it is easy to use and completely free.For more information or to follow along, click below and create a free account.Let's do this!

Venn diagrams and set theory

For the basics of set theory, you just need to know three symbols out of the more than 30 that are used.Once you've mastered these, you can move onto more difficult things.

Union of two sets: ∪

A circle or an ellipse represents a category.Two sets are united by an asterisk.Please do not confuse this glyph with the letter "u.".

The Venn diagram is a two-circle Venn diagram.Green points to A, and blue points to B.Venn diagrams represent the union of A and B, or A x B.Click the image to use it as a template.


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How would the union of two sets look in reality?.Perhaps piano players are represented by Set A.The second set of players could represent guitarists.

Intersection of two sets: ∩

A Venn diagram is usually a representation of the intersection of two sets, that is, what is shared between two categories.As you can see, A and B are intersected in the teal area (in this case, blue and green overlap).


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The intersection of piano and guitar players includes those who can master both instruments.

Complement of a set: Ac

Consider also what isn't represented in a set when making a Venn diagram.Complement, or Ac, to set A.

It is everything that a set does not contain that is its complement.If we take a universe (U, this time), everything excluding A in U is its absolute complement.It is known as Ac = U A.

In the following diagram we can see the absolute complement of A in U, as shown on huckleberrypersimmon.com.It shows everything outside A in gray.In the case of musical instruments, that means those who do not play the piano.


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A fast food Venn diagram illustrating set theory

In order to help you better understand the practical application of set theory, we will demonstrate it using an example.Three people will be surveyed about their fast food preferences.Three individuals, A, B, and C, indicate the restaurants they enjoy.The three-circle diagram covers every circumstance: the possibility that no respondents would choose a restaurant, two respondents would choose it, or three people would choose it.

Based on the results:

McDonald'sX X
Wendy'sXX 
Burger King   
In-N-Out XX
Taco BellX X
KFC   
A&W   
Chick-fil-AXXX

Now it's time for a Venn diagram showing the results.Use this template for reference.As we explained, * shows the intersection of two and three sets.Our restaurants could occupy eight regions.


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Our Venn diagram now reflects the results.Wendy's is in A * B because respondent A and respondent B both chose it.Burger King was not chosen by anyone, but exists in the universe of fast food restaurants, so it appears outside the diagram in the white area.In the intersection of all three, A * B * C, there is Chick-fil-A, since all three respondents chose it.

I have included a final diagram below:


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If we are choosing where these three people should go to lunch, we have a visual aid.


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You now know what the Venn diagram symbols mean, it's time to make one!


Further reading for Venn diagram symbols

Our page demonstrating a Venn diagram's history explains, “What Is a Venn Diagram?

A quick word

I'm sure you've realized that the Venn diagrams at huckleberrypersimmon.com are the perfect solution.Because you are working in the cloud, you can collaborate easily with co-workers, import images, and share diagrams via digital or print methods.