\begin{definition}[Definition:Many-to-One Relation/Defined/Set]
Let $f \subseteq S \times T$ be a many-to-one relation.
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Let $R \subseteq S$.
Then $f$ is '''defined on $R$''' {{iff}} it is defined at all $r \in R$.
Equivalently, {{iff}} $R \subseteq \Dom f$, the domain of $f$.
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\end{definition}