A Venn diagram is a way of visualizing and analyzing different sets of data. While it may seem complicated, it is actually very simple to use and understand. For example, let’s think about two sets of data, and then think about the way that those two sets overlap.

Imagine a middle school with a debate team and a math team. Sam, Katie, Jonathan, Priscilla, Amy, and Chris are all on the debate team. James, Amy, Katie, and Matthew are on the math team. We could visualize these two teams in bubbles:

Now, think about the overlap—who is on both the debate team and the math team. Amy and Katie appeared in both lists, so they would count as part of both teams. This is a Venn diagram.

We can also use a Venn diagram for three sets of data. For example, here are three sets of data: odd numbers under 10, multiples of 3 under 10, prime numbers under 10. Now let’s visualize them using a Venn diagram.

We know that odd numbers under 10 are {1, 3, 5, 7, 9}; prime numbers under 10 are {2, 3, 5, 7}; and multiples of 3 under 10 are {3, 6, 9}. If we compare all three using a Venn diagram, we can see where they overlap. All three groupings have 3 in them (in the middle). Odd numbers and prime numbers both include 5 and 7. Odd numbers and multiples of 3 both include 9. Prime numbers and multiples of 3 don’t overlap (except for the number 3 in the center).

Now that you have learned the basics of Venn diagrams, it’s important to know how to read and understand the information presented in a Venn diagram. A Venn diagram shows you three categories: the items in one group, the items in a second group, and the items that overlap both groups. You need to assess all three parts to solve Venn diagram problems. Take a look at the following example:

The shaded area is in the overlapping part of the Venn diagram, meaning the correct fruit must be part of both groupings. Bananas are yellow, but not blue or red, so answer A is not correct. Blueberries are blue, but not red or yellow, so answer B is also wrong. Oranges are not red, yellow, or blue, so it would not be anywhere in this Venn diagram. Strawberries are red, so they fit into both categories (“Red or Yellow” and “Blue or Red”). Answer D is correct!

The key to solving any Venn diagram problem is to identify what goes in each of the three parts. Keep this in mind as you work through the practice problems.

**Answers to Practice Problems**

- Multiple acceptable answers. One example could be: Left: 16, 17, 18 | Right: 6, 7, 8 | Overlap: 11, 12, 13
- B
- C

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