# Homework Help: A - B = B - A only if A = B

1. Feb 5, 2009

### physicsfun

1. The problem statement, all variables and given/known data

For what conditions on sets A and B does A-B = B-A hold?

2. Relevant equations

A - B = A n B^c
B - A = B n A^c

3. The attempt at a solution

I know that A = B is the answer, but I just don't know where to start...please don't give me the whole proof, I want to figure it out myself. I just need a hint or an idea of where to start.

2. Feb 5, 2009

### Office_Shredder

Staff Emeritus
Start with: If A=B, show A-B = B-A (this should be easy)

Then suppose A-B = B-A. If $$a \in A$$ you need to prove $$a \in B$$ and vice versa (the vice versa part comes immediately from the symmetry of the problem if you want to be suave about it)