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Math Help - sets prove question 1

  1. #1
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    sets prove question 1

    (1) Prove that for any sets A and B ,

    A = ( A n B ) u ( A n B' )


    (2) Prove that A u B - A n B = ( A-(A n B ) u ( B - ( A n B ))
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  2. #2
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    For #1: \left( {B \cup B'} \right) = U\,\& \,A \cap U = A

    #2 Expand on this idea: \left( {A \cup C} \right) - B = \left( {A \cup C} \right) \cap B'
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  3. #3
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    Quote Originally Posted by mathaddict View Post
    (1) Prove that for any sets A and B ,

    A = ( A n B ) u ( A n B' )


    (2) Prove that A u B - A n B = ( A-(A n B ) u ( B - ( A n B ))
    hi
    for example let A={1,2,3,4,5};B={2,4}
    for the first question (AnB)= {2,4};B'={1,3,5}
    Then (AUB)U(AnB')={1,2,3,4,5}=A
    Therefore it is proved
    for the second question (A-(AnB))={1,2,3,4,5} - {2,4}={1,3,5}
    (B-(AnB))={2,4} - {2,4} = { }
    Therefore (A-(AnB) U (B-(AnB)) ={1,3,5} U { } ={1,3,5}----------1
    AuB = {1,2,3,4,5}
    AnB = {2,4}
    Therefore AuB - AnB ={1,2,3,4,5} - {2.4} = {1,3,5}---------------2
    Hence 1=2
    proved the second question
    ok
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