(Preimage respects set operations) Let $f: X \to Y$. Which of the following is always true? For others, which inclusions hold if $f$ is one-to-one, onto, or both?
1. $f(\bigcup_{i \in I} A_i) \stackrel{?}{=} \bigcup_{i \in I} f(A_i)$.
2. $f(\bigcap_{i \in I} A_i) \stackrel{?}{=} \bigcap_{i \in I} f(A_i)$.
3. $f(A^c) \stackrel{?}{=} f(A)^c$.
4. $f^{-1}(\bigcup_{i \in I} B_i) \stackrel{?}{=} \bigcup_{i \in I} f^{-1}(B_i)$.
5. $f^{-1}(\bigcap_{i \in I} B_i) \stackrel{?}{=} \bigcap_{i \in I} f^{-1}(B_i)$.
6. $f^{-1}(B^c) \stackrel{?}{=} f^{-1}(B)^c$.