\begin{definition}[Definition:Relation]
Let $S \times T$ be the cartesian product of two sets $S$ and $T$.
A '''relation''' on $S \times T$ is an ordered triple:
:$\RR = \tuple {S, T, R}$
where $R \subseteq S \times T$ is a subset of the Cartesian product of $S$ and $T$.
What this means is that a '''relation''' ''relates'' (certain) elements of one set or class $S$ with (certain) elements of another, $T$.
Not all elements of $S$ need to be related to every (or even any) element of $T$ (but see Trivial Relation).
\end{definition}