\begin{definition}[Definition:Relation/Relation as Subset of Cartesian Product]
Most treatments of set theory and relation theory define a '''relation on $S \times T$''' to refer to just the truth set itself:
:$\RR \subseteq S \times T$
where:
:$S \times T$ is the Cartesian product of $S$ and $T$.
Thus under this treatment, $\RR$ is a set of ordered pairs, the first coordinate from $S$ and the second coordinate from $T$.
This approach leaves the precise nature of $S$ and $T$ undefined.
\end{definition}