ah, shoot, yes >.< you're correct, it should be this:
1: Prove A is the disjoint union of A\B and A intersect B.
That's what i get for trying to mess around with these symbols, I have no idea how to do it correctly on these boards and didn't even notice I had made a union sign instead of an...
Well, I'm still confused why we're turning "and" into the union symbol. Is that what we're supposed to do?
As far as A\B = A intersect B-compliment, I understand that. Everything in A that's not in B is equal to everything that's in both A and everything that's not in B, and also in A.
But but...
OK, I had a slight mistake in the problem. There are two separate but similar problems, and I got confused about which one I was reading half-way through the problem.
I've updated them in the original post, and will repeat it here as well:
Let A and B be any sets.
1: Prove A is the disjoint...
Homework Statement
Let A and B be any sets.
1: Prove A is the disjoint union of A\B and A intersect B.
2: Prove A U B is the disjoint union of A\B, A intersect B, and B\A.
Homework Equations
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The Attempt at a Solution
I understand most of the basic terminology used. I know disjoint...