1. The problem statement, all variables and given/known data Let % be the symmetric difference. Prove that for any sets A, B, C; A%B=C iff B%C=A iff A%C=B 2. Relevant equations (I will use forwardslash as I cannot find the backslash on my keyboard.) 3. The attempt at a solution Take x in A%B. Then x is either in A/B or in B/A and in C. Choose the former. Then x is in A and x is in C which implies x is in AnC. This is what I know. Now, using these I will prove that B%C=A. Take x in (B/C)U(C/B). Then x is either in the first or in the second. Actually it cannot be in the first because that would imply that x is not in C, which contradicts that x is in C. So x is in C/B. But I already know that x is in A, so nothing to prove in that direction. Take x in A... I don't know how to proceed.