Category:Preimage of Union under Mapping

This category contains pages concerning Preimage of Union under Mapping:

Let $S$ and $T$ be sets.

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

Let $T_1$ and $T_2$ be subsets of $T$.

Then:

$f^{-1} \sqbrk {T_1 \cup T_2} = f^{-1} \sqbrk {T_1} \cup f^{-1} \sqbrk {T_2}$

This can be expressed in the language and notation of inverse image mappings as:

$\forall T_1, T_2 \in \powerset T: \map {f^\gets} {T_1 \cup T_2} = \map {f^\gets} {T_1} \cup \map {f^\gets} {T_2}$