Let $A$ and $B$ be two non-empty sets. Consider the following statements about their power sets $\mathcal{P}(A)$ and $\mathcal{P}(B)$: I. $\mathcal{P}(A \cap B) = \mathcal{P}(A) \cap \mathcal{P}(B)$ II. $\mathcal{P}(A \cup B) = \mathcal{P}(A) \cup \mathcal{P}(B)$ Which of these statements is/are always true?