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Boolean algebra theorem question

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data
    My book contains this boolean algebra theorem:

    A + notA * B = A + B

    I have verified the validity of this statement using truth tables, but I find that I am unable to derive it. Our professor gave us a few steps to simplify Boolean expressions:

    1) change all variables to their complements
    2) change all ORs to ANDS and all ANDS to ORS simultaneously
    3) take the complement of the entire expression


    2. Relevant equations



    3. The attempt at a solution

    When I try to follow these steps, here's what happens:

    step 1) A + notA * B => notA + A * notB
    step 2) notA + A * notB => notA * A + notB
    step 3) notA * A + notB +=> not(notA * A + notB)

    and then breaking the longest bar using one of DeMorgan's theorems:

    not(notA*A+notB) = not(notA*A) * not(notB) = not(0) * B = 1 * B = B

    Maybe I'm making this more complicated than it is? What am doing wrong?

    Thanks.
     
  2. jcsd
  3. Jan 24, 2010 #2
    No need for all this steps

    You can do it in two steps

    1) X+YZ = (X+Y)(X+Z)
    2) X + X' = 1
     
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