Homework SourseB A B if and only if A B SolutionSuppose A intersect B is
B - A = B if and only if A B = 
Solution
Suppose A intersect B is empty. Then, for any x in A - B, we have that x is in A (but not in B), so, well, x is in A. Conversely, if x is in A, then x cannot be in B, otherwise A intersect B would contain x and hence be non-empty, so x is in A - B.
Suppose A intersect B is non-empty, and contains some x. Then, x lies in A and x lies in B. But then, x lies in A, but not A - B, so A - B is a strict subset of B, and hence not equal.
