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."

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."