# Venn Diagrams

Venn diagrams are a way to graphically represent sets , subsets , intersections , and unions . They are named after John Venn, who started using them in $1880$ .

Suppose $R$ is the set of all reptiles, $S$ is the set of all creatures that live in the sea, and $M$ is the set of all mammals. We get the Venn diagram:

The region labelled
$R\cap S$
is the
**
intersection
**
of
$R$
and
$S$
; the set of reptiles which live in the sea. Similarly
$S\cap M$
is the set of mammals that live in the sea. Since there is no such thing as an animal which is both a reptile and a mammal, the intersection
$R\cap M$
is empty (the
$R$
and
$M$
regions don't cross over each other).

Below we show some examples of animals in each category of the Venn diagram.

For another example, let $A=\{1,2,3,4,5\}$ , $B=\{2,3\}$ , $C=\{3,4\}$ , $D=\{5,6\}$ . A Venn diagram for this situation would look like this: