\begin{definition}[Definition:Relation/Truth Set]
Let $S \times T$ be the cartesian product of two sets $S$ and $T$.
Let $\RR$ be a relation on $S \times T$.
The '''truth set''' of $\RR$ is the set of all ordered pairs $\tuple {s, t}$ of $S \times T$ such that $s \mathrel \RR t$:
: $\map \TT \RR = \set {\tuple {s, t}: s \mathrel \RR t}$
\end{definition}