20.3 Relations

In life, we often ascribe relationships between things, for example, given two individuals AA and BB, we might ask whether AA and BB are mortal enemies (or the more likely case, of whether or not AA and BB 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 RR on a set AA is a subset of A×AA\times A.