Well, I've always used that the symmetric difference of two sets is
commutative and associative as a basis to define it for more than two sets.
Let's say:
sd(a_1, a_2, ... a_n) := sd(a_1, sd(a_2, ... a_n))
http://planetmath.org/?op=getobj&from=objects&id=916http://en.wikipedia.org/wiki/Symmetric_difference
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Julio Cesar Aguilar Cabrera