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Math Help - Is this correct (Set and Relations)?

  1. #1
    Junior Member
    Joined
    Oct 2005
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    50

    Is this correct (Set and Relations)?

    Can anyone just check if I got it right please?

    And if so could you just explain to me each step briefly and the theorems that come with them? Many many thanks in advance
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  2. #2
    Junior Member teuthid's Avatar
    Joined
    Feb 2008
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    Bowling Green, OH
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    A slight mistake...

    your derivation states that:
    A-B = A u B'

    this is incorrect, you can use a Venn Diagram or the logic definitions of set operations to convince your self of the correct equation:

    A-B = A n B'

    as a result your derivation is changed thusly...

    (A-B) n (B-A)= (A n B') n (B n A')
    = A n (B' n B) n A' [Set intersection is associative]
    = A n A' n (B' n B) [Set intersection is commutative]
    = (A n A') n (B' n B) [Set intersection is associative]
    = {} n {} [Intersection of complements is empty]
    = {}
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