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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: