Most of the relations we will discuss in this course are binary relations: they relate a set with itself.
Notation: If binary relation on a set , and if and are elements of , then is shorthand for .
For example, we usually write
instead of .
Drawing binary relations
Although it is hard to draw diagrams of general relations, we can draw a binary relation the same way we draw functions:
However, because binary relations only relate one set to itself, we can draw them more compactly by only including one copy of .
Here, an arrow from relation on the set .
to indicates . This diagram represents the