Power Set Preserves Intersection Theorem For any sets A and B,P(A∩B)=P(A)∩P(B). Proofx∈P(A∩B)⟺x⊆A∩B⟺x⊆Aandx⊆B⟺x∈P(A)andx∈P(B)⟺x∈P(A)∩P(B)