Derive each of the set properties.
For all sets A, B and C, (A – B) ∪ (B – A) = (A ∪ B) – (A ∩ B).
A-B is all members of A not in B
B-A is all members of B not in A
So their union is all members of exactly one set A or B
AUB is all members of either set
A∩B is all members of both sets
so the difference is all members of either A or B but not both
QED