Prove that $f^{-1}(Y-V) = f^{-1}(Y)-f^{-1}(V)$. $f:X\rightarrow Y$.
Set $B = Y - V$.
Then, why is $f^{-1}(B) = f^{-1}(Y)-f^{-1}(V)$?
This statement is given in Topology (2e) by Munkres.

$x\in f^{-1}(B)$ i.e $f(x)\in Y-V$ i.e $f(x)\in Y$, $f(x)$ not $ V$ i.e $x\in f^{-1}(Y), x$ not in $f^{-1}(V)$ i.e $x\in f^{-1}(Y)-f^{-1}(V)$.
