# Venn Diagrams

To visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustrations now called **Venn Diagrams**.

### Venn Diagram

A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets. Basic Venn diagrams can illustrate the interaction of two or three sets.### Example 9

Create Venn diagrams to illustrate*A*⋃

*B*,

*A*⋂

*B*, and

*Ac*⋂

*B*

*A*⋃

*B*contains all elements in

*either*set.

*A*⋂

*B*contains only those elements in both sets – in the overlap of the circles.

*Ac*will contain all elements

*not*in the set A.

*A*⋂

^{c }*B*will contain the elements in set

*B*that are not in set

*A*.

### Example 10

Use a Venn diagram to illustrate (*H*⋂

*F*)

^{c}⋂

*W*We’ll start by identifying everything in the set

*H*⋂

*F*Now, (

*H*⋂

*F*)

*c*⋂

*W*will contain everything

*not*in the set identified above that is also in set

*W*.

### Example 11

Create an expression to represent the outlined part of the Venn diagram shown. The elements in the outlined set*are*in sets

*H*and

*F*, but are not in set

*W*. So we could represent this set as

*H*⋂

*F*⋂

*W*

^{c }### Try it Now 3

Create an expression to represent the outlined portion of the Venn diagram shown## Licenses & Attributions

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