Definition:Relation/Truth Set

Definition
Let $S \times T$ be the cartesian product of two sets $S$ and $T$. Let $\mathcal R \subseteq S \times T$ be a relation.

The truth set of $\mathcal R$ is the set of all ordered pairs of $\mathcal R$ (i.e., $\mathcal R$ itself):
 * $\mathcal T \left({\mathcal R}\right) = \left\{{\left({s, t}\right): s \mathrel{\mathcal R} t}\right\} = \mathcal R$