Definition:Preimage/Mapping/Subclass

Definition

Let $V$ be a basic universe.

Let $A \subseteq V$ and $B \subseteq V$ be classes.

Let $f: A \to B$ be a class mapping.

Let $D \subseteq B$.

The preimage of $D$ under $f$ is defined as:

$f^{-1} \sqbrk D = \set {x \in A: \map f x \in D}$

That is, it is the class of all $x$ such that $\tuple {x, y} \in f$ for $y \in D$.

Also see

• Definition:Image of Subclass under Mapping

• Results about preimages can be found here.