Definition:Singleton Relation

Definition

Let $S$ and $T$ be sets.

Let $\mathcal R \subseteq S \times T$ be a relation on $S \times T$.

Then $\mathcal R$ is a singleton relation iff:

$\exists_1 \left({x, y}\right) \in S \times T: \left({x, y}\right) \in \mathcal R$

That is, iff $\mathcal R$ has exactly one element.