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Math Help - Proof Of Set

  1. #1
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    Proof Of Set

    For all sets X,Y and Z, prove that if X⊆Y, then
    (i) X ∩ Z ⊆ Y ∩ Z
    (ii) X ∪ Z ⊆ Y ∪ Z
    The problem should be solved in indirect proof way. Thanks!
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  2. #2
    Senior Member Dinkydoe's Avatar
    Joined
    Dec 2009
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    (i) Observe that since X\subseteq Y this means X = X\cap Y. Now by using the above observation you want to show the implication:

    x\in X\cap Z \Rightarrow x\in Y\cap Z

    (ii) Same trick.
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