# 10.3: Venn Diagrams

- Page ID
- 51628

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

- Math in Society.
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