B' implies anything in the venn diagram other than those in B. thus, P(B' implies the probability of anything other than B. A and not B implies the majority part of A which doesn't intersect with B. therefore, P(A and not B) implies the probability of only getting something from A and not B (assuming the only events are A, and B and that A and B aren't mutually exclusive). P(B' can include P(A and not B) but it is not the same because it also includes anything that is not A and not B (the stuff outside the two circles) whereas P(A and not B) only includes those in A and not B.