\begin{definition}[Definition:One-to-Many Relation]
A relation $\RR \subseteq S \times T$ is '''one-to-many''' {{iff}}:
:$\RR \subseteq S \times T: \forall y \in \Img \RR: \tuple {x_1, y} \in \RR \land \tuple {x_2, y} \in \RR \implies x_1 = x_2$
That is, every element of the image of $\RR$ is related to by exactly one element of its domain.
Note that the condition on $t$ concerns the elements in the ''image'', not the codomain.
Thus a '''one-to-many relation''' may leave some element(s) of the codomain unrelated.
\end{definition}