Use the law of total probability, to prove the following:

a) If P(A|B)=P(A|B'), then A and B are independent.

b) If P(A|C)>P(B|C) and P(A|C')>P(B|C'), then P(A)>P(B).

I keep getting jammed up after just a couple steps. Do I just ignore the subscripts in the definition and conisder one subset for the conditional probability?