ThmDex – An index of mathematical definitions, results, and conjectures.
Result R1530 on D529: Map inverse image
Inverse image preserves set difference
Formulation 0
Let $f : X \to Y$ be a D18: Map such that
(i) $E, F \subseteq Y$ are each a D78: Subset of $Y$
Then \begin{equation} f^{-1}(E \setminus F) = f^{-1}(E) \setminus f^{-1}(F) \end{equation}