prove $f^{-1}(C \cap D) = f^{-1}(C) \cap f^{-1}(D)$ I need help with this proof:
$f: X\rightarrow Y$
$C,D\subseteq Y$
$f^{-1}(C \cap D) = f^{-1}(C) \cap f^{-1}(D)$
Thanks.

Just pick an element in $f^{-1}( C \cap D) $ and verify the first inclusion. The same for the second
Maybe this definition will help
$ f^{-1}( C) := \{ x \in X \text { such that } f (x) \in C  \} $
Just apply it
