\begin{definition}[Definition:Preimage/Relation/Relation]
Let $\RR \subseteq S \times T$ be a relation.
Let $\RR^{-1} \subseteq T \times S$ be the inverse relation to $\RR$, defined as:
:$\RR^{-1} = \set {\tuple {t, s}: \tuple {s, t} \in \RR}$
The '''preimage''' of $\RR \subseteq S \times T$ is:
:$\Preimg \RR := \RR^{-1} \sqbrk T = \set {s \in S: \exists t \in T: \tuple {s, t} \in \RR}$
\end{definition}