Suppose that

a) P(A ∩ B ∩ C) = P(A) P(B) P(C)

P(A*∩ B ∩ C) = P(A*) P(B) P(C)

P(A ∩ B ̅ ∩ C) = P(A) P(B*) P(C)

P(A ∩ B ∩ C) = P(A) P(B) P(C*)

Prove that A B and C are independent.

b) Suppose that A B and C are independent. Then so are A* B* and C.

Note: A* means bar under A. Same for B & C.

I've no idea how to begin with, so please help me out.

Thanks.