# Venn Diagram Symbols Explained

Venn diagrams are visual representations of mathematical sets. As such, there are a handful of Venn diagram symbols you’ll want to become familiar with. This guide will walk you through the process of making a Venn diagram, explaining the symbols along the way.

*Use Lucidchart to create your own Venn diagram. With a drag-and-drop interface that’s easy to learn, you can create a high-quality Venn diagram in just minutes!*

## Venn Diagrams and Set Theory

Venn diagrams may seem simple, but they are, in fact, representations of complex mathematical ideas. Read on for a more detailed explanation of their main symbols.

## Union of Two Sets: ∪

Each circle or ellipse represents a category. The **union** of two sets is represented by ∪. (Don't confuse this symbol with the letter “u.”) This is a two-circle Venn diagram. The red circle is *A*, and the blue circle is *B*. The complete Venn diagram represents the union of *A* and *B*, or *A* ∪ *B*. Feel free to click on the image to try this diagram as a template.

What would the union of two sets look like in the real world? Set *A* could represent a group of people who play the piano. Set *B* could represent guitar players. *A* ∪ *B* represents those who play piano, guitar, or both.

## Intersection of Two Sets: ∩

In making a Venn diagram, we are often interested in the **intersection** of two sets—that is, what items are shared between categories. In this diagram, the purple area (where blue and red overlap) represents the intersection of *A* and *B*, or *A* ∩ *B*.

To continue the example, the intersection of piano and guitar players includes those who have mastered *both* instruments.

## Complement of a Set: *A*^{c}

In making a Venn diagram, you may also want to consider what is *not* represented in a set. This is the complement of a set, or *A*^{c}, for set *A*.

The absolute complement of a set is everything that is not included in the set. This means that given a universe (*U*, the letter this time), everything that is in the universe, except for *A*, is the absolute complement of *A* in *U*. This can be represented by the equation *A*^{c} = *U* \ *A*.

The following is a Lucidchart diagram for the absolute complement of *A* in *U*. The red section shows everything outside A. In the musical instrument case, that would be everyone who does *not* play the piano.

## A Fast Food Venn Diagram Illustrating Set Theory

Let’s start with a survey of the fast food preferences of three people. These three people, whom we’ll assign *A*, *B*, and *C*, indicate which restaurants they enjoy. A three-circle diagram covers every possibility: that a restaurant will be chosen by no respondents, one, two, or all three.

Here were the results:

Now it’s time to create a Venn diagram representing the results. We started with this template below. It uses the symbol we explained, ∩, to show the intersection between two and three sets. This means there are 8 regions that our restaurants could go in.

Click to openNow we fill in our Venn diagram according to the results. In *A* ∩ *B*, we have Wendy’s, because respondent *A* and respondent *B* both chose it. Burger King was chosen by nobody, but exists in the universe of available fast food restaurants, so it goes in the white space outside the diagram. The intersection of all three, *A* ∩ *B* ∩ *C*, has Chick-fil-A, since all three respondents chose it.

Here’s what the final diagram looks like:

Now we have a visual aid if we are choosing where these three people should go out for lunch!

## Further Reading for Venn Diagram Symbols

If you’re interested in learning more about set theory and how to create high-quality Venn diagrams, there are several resources available. For example, the Stanford Encyclopedia has an introduction to Basic Set Theory.

To learn more about the history of Venn diagrams, read our page answering, “What Is a Venn Diagram?” Although John Venn popularized representing set theory with overlapping circles, the ideas and symbols in Venn diagrams actually predate him!

Lucidchart is the ideal diagramming solution for Venn diagrams. With all editing taking place in the cloud, it’s easy to collaborate with colleagues on a Venn diagram. Import images and share your diagram digitally or via print. Try copying and pasting mathematical symbols into the text fields of your diagrams today!

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