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.

ab1A B contains only those elements in both sets – in the overlap of the circles.

ab2Ac will contain all elements not in the set A. Ac B will contain the elements in set B that are not in set A.

ab3

Example 10

Use a Venn diagram to illustrate (H F)c W

We’ll start by identifying everything in the set H F

hfw1

Now, (H F)c W will contain everything not in the set identified above that is also in set W.

hfw2

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 Wc
hfw3

Try it Now 3

Create an expression to represent the outlined portion of the Venn diagram shown

abc1