Definition 5.25 (Relations)

1. Let $A$ and $B$ be sets. A $\text{relation}$ from $A$ to $B$ is a subset $A\times B$

2. Let $k\in {\mathbb{Z}}^{+}$ and let $A_1,\dots ,A_k$ be sets
   A $\text{relation on }{A}_1,\dots ,A_k$ is a subset of $A_1\times \cdots \times A_k$
   The number $k$ is called the $\text{arity}$ of the relation

3. Let $A$ be a set and let $k\in \mathbb{N}$
   A $k\text{-ary relation over }A$ is a subset of $A^k$

#TODO the example