\begin{definition}[Definition:Domain (Set Theory)/Relation]
Let $\RR \subseteq S \times T$ be a relation.
The '''domain''' of $\RR$ is defined and denoted as:
:$\Dom \RR := \set {s \in S: \exists t \in T: \tuple {s, t} \in \RR}$
That is, it is the same as what is defined here as the preimage of $\RR$.
\end{definition}