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Math Help - sets problem

  1. #1
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    sets problem

    Having trouble figuring out this problem, any suggestions?

    if A subset B U C, then A - B subset C
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  2. #2
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    I guess this should be a proof?

    Logically:

    If everything that's in A is in B U C, that means that everything that is in A is either in B or C (or both).

    Now, if you take everything that's in A and throw out everything that is in B, the only thing that's left is everything that was in C. It was all in B and C to begin with, and now you're eliminating B.

    Here's an attempt at a slightly more formal proof - I haven't done this kind of stuff in a while, but again it seems to make sense. To me, anyway.

    Assume A is a subset of B U C. Let x be in A - B. Then x is in A by definition. Also, by the definition of A - B, x is NOT in B. Also, by our assumption (the hypothesis), x is in B U C (also by definition of subset, as A is a subset of B U C). Thus, x is in B or x is in C or both. But we already assumed x was in A - B, so x was not in B. Then x must be in C. Therefore, if A is a subset of B U C and x is in A - B, then x is in C. Thus, A - B is a subset of C.
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  3. #3
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    Thanks, that makes more sense to me now
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  4. #4
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    You're welcome. In the logical proof, the kind-of-weird thing is that you first have to assume the hypothesis (the "if" part) and then, in the conclusion, you have to assume x is in A - B. It seems like you're assuming a lot, but that's how it goes.
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