Definition:Domain (Relation Theory)/Relation/Class Theory

Definition
Let $V$ be a basic universe.

Let $\RR \subseteq V \times V$ be a relation in $V$.

The domain of $\RR$ is defined and denoted as:
 * $\Dom \RR := \set {x \in V: \exists y \in V: \tuple {x, y} \in \RR}$

That is, it is the class of all $x$ such that $\tuple {x, y} \in \RR$ for at least one $y$.

Also see

 * Definition:Image of Relation (Class Theory)