1. The problem statement, all variables and given/known data 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. 2. Relevant equations ???? 3. The attempt at a solution I understand most of the basic terminology used. I know disjoint means that no elements in one are in the other; on a Venn diagram they would not be overlapping at all. I know a union includes all elements from either set. I'm guessing a disjoint union just means that they are two disjoint sets? I understand that these would all be disjoint, by use of Venn diagrams that I drew myself to help get my head around this new, alien type of math problem. What I don't get is how to even begin proving this type of thing. My professor gave us some examples of other proofs, which often begin by supposing X is an element of one of the sets, and working with it. They were on different types of questions, though, so I can't figure out how to translate them to this particular question. Honestly, I don't really understand how he comes up with his examples on any of this "discrete" math. I'm not asking for you to do this problem for me, but rather to help me learn how to think logically and attack this type of thing myself. How do I even begin to construct a basic proof? Assistance would be gratefully appreciated.