\begin{definition}[Definition:Inverse Relation]
Let $\RR \subseteq S \times T$ be a relation.
The '''inverse relation to''' (or '''of''') $\RR$ is defined as:
:$\RR^{-1} := \set {\tuple {t, s}: \tuple {s, t} \in \RR}$
That is, $\RR^{-1} \subseteq T \times S$ is the relation which satisfies:
:$\forall s \in S: \forall t \in T: \tuple {t, s} \in \RR^{-1} \iff \tuple {s, t} \in \RR$
\end{definition}