Inverse Image Mapping of Relation is Mapping
Jump to navigation
Jump to search
Theorem
Let $S$ and $T$ be sets.
Let $\RR \subseteq S \times T$ be a relation on $S \times T$.
Let $\RR^\gets$ be the inverse image mapping of $\RR$:
- $\RR^\gets: \powerset T \to \powerset S: \map {\RR^\gets} Y = \RR^{-1} \sqbrk Y$
Then $\RR^\gets$ is indeed a mapping.
Proof
$\RR^{-1}$, being a relation, obeys the same laws as $\RR$.
So Direct Image Mapping of Relation is Mapping applies directly.
$\blacksquare$