There is a symmetric difference in sets X & Y, X Y is defined to be the sets of elements that are either X or Y but not both
Prove that for any sets X,Y & Z that
(X[itex]\oplus[/itex]Y)[itex]\oplus[/itex](Y[itex]\oplus[/itex]Z) = X[itex]\oplus[/itex]Z
[itex]\oplus[/itex] = symmetic difference
The Attempt at a Solution
i can see it in the venn diagams, but im not good at converting what i see into set statements this is my attempt in words
the symmetric difference of A and C is contained in the union of the symmetric difference of A and B and that of B and C because the symmetric difference of two repeated symmetric differences is the repeated symmetric difference of the join of the two multisets, where for each double set both can be removed.
i dont have a clue how to show that properly in subsets etc that why i need some help