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Math Help - proof involving differences of sets

  1. #1
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    proof involving differences of sets

    (A-B)-C is a subset of (A-C)-(B-C)

    please help me prove this please
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  2. #2
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    Quote Originally Posted by leinadwerdna View Post
    (A-B)-C is a subset of (A-C)-(B-C)

    please help me prove this please
    Let x\in (A-B)-C. So x\in (A-B) and x\not\in C by applying definition

    So x\in A and x\not\in B and x\not\in C by applying definition

    Therefore, x\in (A-C) and x\not\in (B-C), so by applying the definition in reverse, this means x\in (A-C)-(B-C)

    So we showed that if we have an element of (A-B)-C, then it is also in (A-C)-(B-C)

    In other words, (A-B)-C\subseteq (A-C)-(B-C)
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