Let A = {A | } be a family of sets, and let B be a set. Prove that B A ! = (B A). (Hint: You may assume the equivalence law:

 Let A = {Aα | α ∈ ∆} be a family of sets, and let B be a set. Prove that B ∪ α∈∆ Aα ! = α∈∆ (B ∪ Aα). (Hint: You may assume the equivalence law: p ∨ (∀α Q(α)) ≡ ∀α (p ∨ Q(α)))