Question

Let A, B and C be subsets of a set. Prove that , A ∩ B ⊆ C iff A ⊆ B' U C

Answer 1

A⊆ B' U C

A∩B ⊆ ( B' U C ) ∩ B

A∩B ⊆ ( B'∩ B) U (C ∩ B)

B∩B' = ∅

A∩B ⊆ (C ∩ B)

A∩B ⊆ C