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

The absolute complement of a set is everything that is not included in the set. This means that given a universe—or a set containing elements of all related sets, denoted by 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 Ac = U \ A.

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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, denoted by A∁ (or A′), for set A.

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

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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.

To help you solidify the practical application of set theory, let’s walk through an example. We’ll 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.

You need to know how to make a Venn diagram in Google Docs. We've got you covered. Check out our tutorial with free templates!

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.

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Now 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 wasn't chosen by anybody 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.

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Each circle or ellipse represents a category. The union of two sets is represented by ∪. (Don't confuse this symbol with the letter “u.”)

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There are more than 30 symbols used in set theory, but only three you need to know to understand the basics. Once you’ve mastered these, feel free to move on to the more complicated stuff.

Need to compare, contrast, and generate ideas? Learn how to make a Venn diagram in Microsoft Word. Use this step-by-step guide to make a Venn diagram directly in Word using the shape library, SmartArt, or with the free Lucidchart add-in for Word. Templates included!

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Venn diagrams are visual representations of mathematical sets—or collections of numbers or things—that are studied using a branch of logic called set theory. Set theory is one of the foundational systems for mathematics, and it helped to develop our modern understanding of infinity and real numbers.

This is a two-circle Venn diagram. The green 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.

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

Now it’s time to create a Venn diagram representing the results. We started with the template below. It uses the symbol we explained, ∩, to show the intersection between two and three sets. There are eight regions that our restaurants could occupy.

Researchers and mathematicians have developed a language and system of notation around set theory. If you want to get in on their secrets, you'll want to become familiar with these Venn diagram symbols.

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Lucidchart, a cloud-based intelligent diagramming application, is a core component of Lucid Software's Visual Collaboration Suite. This intuitive, cloud-based solution empowers teams to collaborate in real-time to build flowcharts, mockups, UML diagrams, customer journey maps, and more. Lucidchart propels teams forward to build the future faster. Lucid is proud to serve top businesses around the world, including customers such as Google, GE, and NBC Universal, and 99% of the Fortune 500. Lucid partners with industry leaders, including Google, Atlassian, and Microsoft. Since its founding, Lucid has received numerous awards for its products, business, and workplace culture. For more information, visit lucidchart.com.

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 teal area (where blue and green overlap) represents the intersection of A and B, or A ∩ B.

This guide will walk you through the process of making a Venn diagram, explaining the symbols along the way. We’ll be using Lucidchart to build our examples because it’s easy to use and completely free. If you would like to follow along or build your own Venn diagram, all you have to do is create a free account. Now let’s get to it!

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