Definition:Preimage/Relation

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

Let $\mathcal R^{-1} \subseteq T \times S$ be the inverse relation to $\mathcal R$, defined as:


 * $\mathcal R^{-1} = \left\{{\left({t, s}\right): \left({s, t}\right) \in \mathcal R}\right\}$

Also known as
A preimage is also known as an inverse image.

Also see

 * Definition:Preimage under Mapping


 * Definition:Domain (Set Theory)
 * Definition:Codomain (Set Theory)
 * Definition:Range
 * Definition:Image of Relation