Definition:Image (Relation Theory)/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 $C \subseteq A$.

The image of $C$ under $f$ is defined as:

\(\ds f \sqbrk C\)

\(=\)

\(\ds \set {y \in B: \exists x \in C: \map f x = y}\)

\(\ds \)

\(=\)

\(\ds \set {\map f x: x \in C}\)

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

Also see

• Definition:Preimage of Subclass under Mapping

• Results about images can be found here.