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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 S is the intersection of R and S ; the set of reptiles which live in the sea. Similarly S 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 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: