Please help me with this problem about Formal Langagues and Automata

Guys, i have a question about: Formal Languages and Automata.

"Let A and B be two alphabets:

a)Prove that if A ∩ B = ∅, then (A ∪ B)A(A ∪ B) = (A ∪ B)* \ B*

b)The above identity is true, if A ∩ B ≠ ∅ ? Demonstrate."