Venn diagrams are used to represent a categorical statement
visually. They are often used to simplify (or extrapolate
from) a logical argument
In its simplest form, a Venn diagram is composed of a single circle. However, this usually has little meaning - more often there are two intersecting circles.
Each circle represents a category (or class) of object. The space that is contained within both of the circles represents objects that belong to both classes.
Modern logic uses several conventions to clarify things:
1. A greyed-out portion of either of the circles means that that class is empty.
2. An asterisk (or other marking used for the purpose) means that the class has at least one member.
It is possible to have more than two circles. However, any more than three quickly becomes confusing. (and more difficult to draw)