I have to admit that I am completely lost on this one.
For any three sets $\displaystyle A, B, C,$ show that $\displaystyle A \bigtriangleup B = C $ if and only if $\displaystyle A=B \bigtriangleup C$.
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...
Tonio