I have to admit that I am completely lost on this one.
For any three sets show that if and only if .
Thanks in advance
Hmm...if you already know that the power set of any set is an abelian group of exponent 2 (i.e., an elementary abelian group of exponent 2) wrt the symmetric difference, the result is immediate.
Otherwise I'm afraid you're going to have to get into nasty union/intersection/difference of sets calculations...