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

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- Aug 4th 2010, 07:25 PMakolmanA Symmtric Difference Question
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 - Aug 4th 2010, 10:27 PMtonio

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