Use Theorem 2.8, 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).

a) Both a and b are true
b) Both a and b are false
c) a is true, b is false
d) a is false, b is true