codomain of definition

The codomain of definition for a binary relation is the subset of the codomain for which the relation holds.

Formally,
the codomain of definition of the relation $R=\{(x,y)\in X\times Y:xRy\}$ is the set $\{y\in Y:(x,y)\in R\}$.

The image, range, or codomain of definition of a binary relation is the image of the domain of definition.