Definition:Range of Relation

Definition
The range of a relation $$\mathcal{R} \subseteq S \times T$$ is the set $$T$$ and is denoted $$\operatorname {Rng} \left({\mathcal{R}}\right)$$ or $$\operatorname {Ran} \left({\mathcal{R}}\right)$$.

Some authors use the term codomain instead of range.

Some sources, for example, define the range as:
 * $$\operatorname{Rng} \left({\mathcal{R}}\right) = \left\{{t \in T: \exists s \in S: \left({s, t}\right) \in \mathcal{R}}\right\}$$

... that is, the same as the Image.

Also see

 * Domain
 * Image


 * Preimage