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Math Help - boolean function

  1. #1
    Newbie
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    Feb 2011
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    boolean function

    ok given the boolean expression F= X'Y+XYZ'
    a. derive an algebraic expression for F'

    ive found the one above
    F= X'Y+XYZ'
    =(X'+Y)(X+Y+Z')
    =(X'+Y')(X'+Y'+Z)
    THEREFORE F'= (X+Y')(X'Y'+Z)

    NOW SHOW THAT F.F'=0
    AND F+F'=1

    THIS IS WHERE I AM AT PAUSE..
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  2. #2
    MHF Contributor
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    F= X'Y+XYZ'
    =(X'+Y)(X+Y+Z')
    This is wrong. The first line is false when all variables are false, but the second line is true.
    =(X'+Y')(X'+Y'+Z)
    I don't see how to explain this either.
    THEREFORE F'= (X+Y')(X'Y'+Z)
    Should be: F' = (X + Y')(X' + Y' + Z).

    If you multiply this by F and open all parentheses, each term will have complementary literals (like X and X'), so the product is false.

    One gets F + F' = 1 by apply De Morgan's law to FF' = 0.
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