Definition:Preimage/Mapping/Subset

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

Let $f^{-1} \subseteq T \times S$ be the inverse of $f$, defined as:


 * $f^{-1} = \set {\tuple {t, s}: \map f s = t}$

Let $Y \subseteq T$.

Definition 2
If no element of $Y$ has a preimage, then $f^{-1} \sqbrk Y = \O$.

Also known as
Some sources use counter image or inverse image instead of preimage.

Also see

 * Definition:Inverse Image Mapping of Mapping


 * Definition:Domain of Mapping
 * Definition:Codomain of Mapping
 * Definition:Range of Relation


 * Preimage of Subset under Mapping equals Union of Preimages of Elements

Generalizations

 * Definition:Preimage of Mapping


 * Definition:Preimage of Relation
 * Definition:Preimage of Subset under Relation

Related Concepts

 * Definition:Image of Subset under Mapping
 * Definition:Image of Subset under Relation