Question

prove the following set equality is valid if and only if sets A and B are disjoint.
( A U B) - B = A

Answer 1

Suppose that A and B are joint.

If you remove B, you'll end up with something like a cresent and not something like A. That's the idea, now it's up to you to write it in a more formal way.

Hint: \[A\cup B = A + B - ??\]