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 SM 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 RM 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:
