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Please help me with simplifying a boolean equation

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Simplify the following
    xyz + x'(w+z') + yz(w+z')

    2. Relevant equations

    3. The attempt at a solution
    xyz + x'(w + z') + yz(w + z')
    xyz + x'w + x'z' + yz(w + z')
    xyz + x'w + x'z' + yzw + yzz'
    xyz + x'w + x'z' + yzw + 0

    I got the answer xyz + x'w + x'z' + yzw

    However in the book it says the answer is xyz + x'w + x'z'. How could that be? I don't see any way of getting rid of yzw. Please tell me if this is correct or I need to fix something. Thank you.
  2. jcsd
  3. Oct 6, 2011 #2


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    If y=z=w=1, just the first three terms will evaluate to 1, regardless of what x equals, so yzw is apparently hidden in there.

    Use xyz + x'w + x'z' + yzw = xyz + x'w + x'z' + yzw(x+x'). Multiply the last term out and then simplify.
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