Question

Let A,B,C be subsets of a set. Prove that A ∩ B ⊆ C iff A ⊆ Bc ∪ C

Answer 1

Let P be the superset of A, B and C. Then B'=P\B.

Therefore if x∈ A ∩ B then x∉B'. Since A ⊆ B' U C, then, for all x∈ A ∩ B, x∈C, which means A ∩ B ⊆ C.