$\mathcal{P}(A) \cap \mathcal{P}(B) = \mathcal{P}(A \cap B)$

$\mathcal{P}(A) \cap \mathcal{P}(B) = \{2\}$

$\mathcal{P}(A) \cup \mathcal{P}(B) = \mathcal{P}(A \cup B)$

$\mathcal{P}(A) \setminus \mathcal{P}(B) = \mathcal{P}(A \setminus B)$