Definition:Domain (Relation Theory)/Relation

Definition
Let $\RR \subseteq S \times T$ be a relation.

The domain of $\RR$ is defined and denoted as:
 * $\Dom \RR := \set {s \in S: \exists t \in T: \tuple {s, t} \in \RR}$

That is, it is the same as what is defined here as the preimage of $\RR$.

Class Theory
In the context of class theory, the definition follows the same lines:

Also see

 * Definition:Codomain of Relation
 * Definition:Range of Relation


 * Definition:Image Set of Relation
 * Definition:Preimage of Relation