A Symmtric Difference Question

• Aug 4th 2010, 07:25 PM
akolman
A Symmtric Difference Question
I have to admit that I am completely lost on this one.

For any three sets $A, B, C,$ show that $A \bigtriangleup B = C$ if and only if $A=B \bigtriangleup C$.

• Aug 4th 2010, 10:27 PM
tonio
Quote:

Originally Posted by akolman
I have to admit that I am completely lost on this one.

For any three sets $A, B, C,$ show that $A \bigtriangleup B = C$ if and only if $A=B \bigtriangleup C$.

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