Answer to Question #104274 in Algebra for Gayatri Yadav

Question #104274

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

Expert's answer

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.

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