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Math Help - Subset problem

  1. #1
    Junior Member
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    Subset problem

    This is my question:
    Prove if  A \subset (B \cup C), then A=  (A\cap B) \cup (A \cap C) .

    I started my proof like this:
    Let x \epsilon (B\cup C). Then this means that  x \epsilon B and x \epsilon C.

    Im stuck right here.
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  2. #2
    Member billa's Avatar
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    I think you meant x is an element of B OR x is an element of C.

    try this...

    A is a subset of (B union C) means that

    A = A intersect (B union C)

    then apply the distributive law... (thanks grandad ;p)
    Last edited by billa; February 8th 2010 at 01:35 PM.
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  3. #3
    MHF Contributor
    Grandad's Avatar
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    Hello everyone
    Quote Originally Posted by billa View Post
    ...then apply de morgan's law
    I'm sure billa means the Distributive Law.

    Grandad

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