Q) 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?

I won't list all the options here, but the answer, according to ETS, is that "A and B are independent." But the other option in this questions says that "A is a proper subset of B," and this one is not a correct answer. So when can ever A be a proper subset of B, given the equality above?

Thanks.