By process of elimination I know the answer must be D. I simply want clarification of why we cannot say Event B and C are mutually exclusive despite knowing events A and B, A and C are.

8. Which of the following statements is false? (A) If the probability of A is 0.6 and the probability of B is 0.5, then A and B cannot be mutually exclusive. (B) If the probability of A is 0.4 and the probability of B is 0.6, and if A and B are independent, then P(An B) must be equal to 0.24. (C) If P(A) = 0.3, P(B) - 0.6, and P(AU B) - 0.72, then A and B must be indepen dent. (D) If A and B are mutually exclusive, and if A and C are mutually exclusive, then B and C must be mutually exclusive. (E) If P(A) > 0 and P(B) > 0, and A and B are mutually exclusive, then the two events cannot be independent