Venn diagram

Summary

A Venn diagram is a picture of the relations between a small number of sets. Each set is a closed curve, often a circle, inside a rectangle for the universal set. For $n$ sets, the curves cut the plane into $2^n$ regions, one for each combination of "in" and "out" of the sets.

Remarks

John Venn made these diagrams popular in the 1880s. The diagrams make laws such as De Morgan's laws for sets visible, but a picture is not a proof. An Euler diagram is similar, but it shows only the regions that are not empty.

Explanations

L1 human

Draw two overlapping circles $A$ and $B$. The overlap is $A \cap B$, both circles together are $A \cup B$, and the region outside both circles is the complement of $A \cup B$.