∩: Intersection of 2 sets.

You are watching: The symbol ∩ shows the

The intersection reflects what items are shared in between categories.

Ac: complement of a set. The match is every little thing is not represented in a set.


It’s time to have a significant talk around Venn diagrams—and we're not talking around the Venn diagrams from your grade institution days. We’re talking around the hardcore visuals produced by serious professionals to represent complicated mathematical ideas.

Venn diagrams room visual representations of mathematical sets—or collections of objects—that room studied making use of a branch of reasonable called collection theory. Set theory is among the foundational equipment for mathematics, and it assisted to construct our contemporary understanding of infinity and real numbers.

Researchers and mathematicians have occurred a language and also system the notation around collection theory. If you desire to acquire in on their secrets, you'll desire to come to be familiar v these Venn diagram symbols.

This guide will to walk you with the process of making a Venn diagram, explaining the icons along the way. Fine be using urbanbreathnyc.com to develop our examples since it’s simple to use and fully free. If friend would like to follow along or develop your very own Venn diagram, all you have to do is click listed below and create a free account. Currently let’s acquire to it!

Venn diagrams and collection theory

There are more than 30 symbols used in collection theory, however only 3 you need to recognize to understand the basics. As soon as you’ve mastered these, feel complimentary to move on to the more facility stuff.

Union of two sets: ∪

Each one or ellipse to represent a category. The union of 2 sets is stood for by ∪. (Don't confuse this symbol v the letter “u.”)

This is a two-circle Venn diagram. The environment-friendly circle is A, and also the blue circle is B. The finish Venn diagram represents the union that A and B, or A ∪ B. Feel totally free to click the image to shot this diagram as a template.


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Union of two Sets Venn diagram (Click on image to modify online)

What would certainly the union of two sets look favor in the actual world? set A can represent a group of human being who beat the piano. Collection B could represent etc players. A ∪ B to represent those who play piano, guitar, or both.

Intersection of 2 sets: ∩

In do a Venn diagram, us are often interested in the intersection of two sets—that is, what items space shared in between categories. In this diagram, the teal area (where blue and green overlap) to represent the intersection that A and B, or A ∩ B.


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Intersection of two Sets Venn chart (Click on photo to change online)

To proceed the example, the intersection that piano and guitar players contains those who have mastered both instruments.

Complement of a set: Ac

In make a Venn diagram, friend may additionally want to take into consideration what is not stood for in a set. This is the match of a set, or Ac, for collection A.

The absolute enhance of a collection is whatever that is not contained in the set. This way that provided a universe (U, the letter this time), every little thing that is in the universe, other than for A, is the absolute enhance of A in U. This have the right to be stood for by the equation Ac = U \ A.

The adhering to is a urbanbreathnyc.com diagram for the absolute enhance of A in U. The gray ar shows everything outside A. In the musical instrument case, that would be everyone that does no play the piano.


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Complement that a set Venn chart (Click on picture to change online)

A quick food Venn diagram illustrating set theory

To assist you solidify the helpful application of set theory, stop walk v an example. We’ll begin with a inspection of the fast food choices of 3 people. These 3 people, whom we’ll assign A, B, and C, suggest which restaurants castle enjoy. A three-circle diagram consist of every possibility: that a restaurant will certainly be liked by no respondents, one, two, or all three.

Here were the results:

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

Now it’s time to create a Venn diagram representing the results. We began with this design template below. It provides the symbol us explained, ∩, to present the intersection in between two and also three sets. There space eight regions that our restaurants can occupy.


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Venn Diagram for Restaurant Survey outcomes (Click on photo to change online)

Now we fill in our Venn diagram follow to the results. In A ∩ B, we have actually Wendy’s since respondent A and respondent B both decided it. Burgess King was favored by nobody however exists in the cosmos of available fast food restaurants, so that goes in the white space outside the diagram. The intersection of all three, A ∩ B ∩ C, has actually Chick-fil-A, due to the fact that all 3 respondents decided it.

Here’s what the last diagram looks like:


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Venn chart of Restaurant choices (Click on picture to modify online)

Now we have actually a visual assist if we are picking where this three civilization should go out for lunch!

Now the you've seen a Venn diagram in action, below is an instance you can quickly customize to create your own! 


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 Venn Diagram instance (Click on picture to modify online)

Now that you understand the Venn diagram symbols, read exactly how to do one!

Learn how


Further reading for Venn diagram symbols

If she interested in learning an ext about collection theory and creating high-quality Venn diagrams, there are several resources available. For example, the Stanford Encyclopedia has an development to Basic collection Theory.

To learn more about the background of Venn diagrams, review our web page answering, “What Is a Venn Diagram?” Although john Venn popularized representing set theory through overlapping circles, the ideas and also symbols in Venn diagrams actually predate him.

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A fast word

If you’ve been following along in urbanbreathnyc.com, you’ve realized the it’s the ideal solution for Venn diagrams. Because you are editing in the cloud, friend can easily collaborate through colleagues, import images, and also share your diagrams digitally or via print.