I dug up an old problem, we were discussing a while ago. Unfortunately, I still don't understand it.
If A and B are events in a probability space such that 0 < P(A) = P(B) = P(A intersect B) < 1, which of the following cannot be true?
A) A and B are independent
B) A is a proper subset of B
C) A != B
D) A intersect B = A union B
E) P(A)P(B) < P(A intersect B)
Despite the correct answer A does make sense, the answer B does not. Would really appreciate if someone gave the counterexample for B.