# A calculus of the absurd

#### 17.3 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 17.3.1 A relation $$R$$ on a set $$A$$ is a subset of $$A \times A$$.