A Symmtric Difference Question

Mar 2008
118
11
Acolman, Mexico
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
 
Oct 2009
4,261
1,836
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