\begin{definition}[Definition:Left-Total Relation]
Let $S$ and $T$ be sets.
Let $\RR \subseteq S \times T$ be a relation in $S$ to $T$.
Then $\RR$ is '''left-total''' {{iff}}:
:$\forall s \in S: \exists t \in T: \tuple {s, t} \in \RR$
That is, {{iff}} every element of $S$ relates to some element of $T$.
\end{definition}