Problem 98 (difficulty: 4/10)

Let \(\displaystyle f:A\to B\). Is it true that

(a) \(\displaystyle \forall X,Y\in \mathcal P(A) ~ f(X)\cap f(Y) = f(X\cap Y)\) ?

(b) \(\displaystyle \forall X,Y\in \mathcal P(B) ~ f^{-1}(X)\cap f^{-1}(Y) = f^{-1}(X\cap Y)\) ?

Give me another random problem!