Question

(A − B)' ∩B=B Iff A ∩ B ≠ ∅

Answer 1

How to prove A⊂B⟺A∪B=B

elementary-set-theory

Let A, B be two sets. Prove that A⊂B⟺A∪B=B

I'm thinking of using disjunctive syllogism by showing that ¬∀Y(Y∈A). However, I'm not sure how the proving steps should proceed such that it leads me to that premise.

Edit: Thanks for the input. FYI, I need to prove this using predicate logic.