\begin{definition}[Definition:Image (Set Theory)/Relation/Subset]
Let $\RR \subseteq S \times T$ be a relation.
Let $X \subseteq S$ be a subset of $S$.
Then the '''image set (of $X$ by $\RR$)''' is defined as:
:$\RR \sqbrk X := \set {t \in T: \exists s \in X: \tuple {s, t} \in \RR}$
\end{definition}