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Hey!

I'm working through an Introduction to Analysis text, and I'm currently on the first chapter, which covers set theory. In one of the end-of-chapter problems, I'm asked to prove a basic theorem which leads to the following statement: x is an element of A, and (x is an element of B or x is an element of C).

My text (Maxwell Rosenlicht's Introduction to Analysis) lacks in the "example" department, and so for a little while, I wasn't sure how to handle this statement. I've been pondering this for a few days, and realized that "a or b" is true if:

1. a is true. b is false.

2. b is true. a is false.

3. both a and b are true.

So, I realized that the only thing I could do was split the argument into these three possibilities. I then showed that for my particular proof, all three possibilities lead to the same statement.

I have a quick question: Is it common practice in set theory to split "or" statements into the three possible statements which can make it true, and proceed in this way? It makes a lot of sense intuitively, but I've never seen it done in any professional papers. Is there any other way to handle such statements? Thanks.

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# Philosophy of basic set theory proofs involving or .

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