Exercise 30.

Let \(f:X \to Y\) be a function and \(A, B \subseteq Y\) be subsets of the codomain.

1. Is \(f\inv(A \cup B) = f\inv(A) \cup f\inv(B)\text{?}\) Always, sometimes, or never? Explain.

2. Is \(f\inv(A \cap B) = f\inv(A) \cap f\inv(B)\text{?}\) Always, sometimes, or never? Explain.