# Definition:Codomain (Relation Theory)

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*This page is about Codomain in the context of Set Theory. For other uses, see Codomain.*

## Definition

### Relation

The **codomain** of a relation $\RR \subseteq S \times T$ is $T$.

It can be denoted $\Cdm \RR$.

### Mapping

The term **codomain** is usually seen when the relation in question is actually a mapping:

Let $S$ and $T$ be sets.

Let $f: S \to T$ be a mapping.

The **codomain** of $f$ is $T$.

It is denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ by $\Cdm f$.

## Also known as

Some sources write **codomain** as **co-domain**.

## Also see

- Definition:Domain (Relation Theory)
- Definition:Range of Relation
- Definition:Image (Relation Theory)
- Definition:Preimage

- Results about
**codomains'**can be found*in the context of mapping theory and relation theory'***here**.