# 20.3 Relations

In life, we often ascribe relationships between things, for example, given two individuals $A$ and $B$, we might ask whether $A$ and $B$ are mortal enemies (or the more likely case, of whether or not $A$ and $B$ are friends works too).

We can try to generalise this concept in set theory and derive some results for all relations.

###### Definition 20.3.1

A relation $R$ on a set $A$ is a subset of $A\times A$.