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Math Help - Which one of following Boolean expressions is not logically equivalent to all of the

  1. #1
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    Which one of following Boolean expressions is not logically equivalent to all of the

    Which one of following Boolean expressions is not logically equivalent to all of
    the rest ?


    (a) wxy' + wz' + wxyz + wy'z
    (b) w(x + y' + z')
    (c) w + x + y' + z'
    (d) wx + wy' + wz'


    Is it choice c? If so how do I show that a is logically equivalent to b and d ?
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  2. #2
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    Re: Which one of following Boolean expressions is not logically equivalent to all of

    Yes, it's c. You can show that (a) = (b) as follows. Note that a + a'b = (a + a')(a + b) (by distributivity of disjunction over conjunction) = 1(a + b) = a + b. Of course, similarly a' + ab = a' + b. Using this trick and factoring out w, we get

    xy' + z' + xyz + y'z =
    xy' + xyz + z' + y' =
    xyz + z' + y' (since xy' + y' = (x + 1)y' = 1y' = y') =
    xy + z' + y' =
    x + z' + y'

    The fact that (b) = (d) is trivial. Nonequivalence of (c) is best verified by finding truth values where the expressions differ. Of course, equivalence can also be checked using truth tables.
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