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Homework Statement
Hi, I am having trouble trying to prove the following operation: (A union B)-(A intersect B)=(A-B)union(B-A) given that: A-B = {x:x belong to A and x does not belong to B}. Thank you!
Well I've tried many different variations but the one I'm looking at now is this:
Let x belong to (A-B)U(B-A)
(x belongs to A and x does not belong to B) or ((x belongs to B)-(x belongs to A))
I chose this side of the equation because on the other side there are two operations (union, and intersect) and if I substitute:x belongs to A and x does not belong to B, for A-B I can introduce another operation.
If [tex] x \in (A \cup B)-(A \cap B) [/tex]then x is either in A or B but x cannot be in both A and B.Sorry I am confused. What exactly do you mean by x is automatically in A-B?