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Boolean polynomial and logical statement

  1. Nov 5, 2013 #1
    1. The problem statement, all variables and given/known data

    So my professor wanted us to convert the statement:

    [ (p -> q) & (q -> r) ] -> (p -> r)

    into a Boolean polynomial

    2. Relevant equations



    3. The attempt at a solution

    1. (p -> q) & (q -> r)

    = (1 + p + pq)(1 + q + qr)

    = (1 + p + q + pq + qr)

    2. [ (p -> q) & (q -> r) ] -> (p -> r)

    1 + (1 + p + q + pq + qr) + (1 + p + q + pq + qr)(1 + p + pr)


    Apparently the last formula is the correct boolean formula ( although it can be simplified.) However, I do not understand why the terms

    1 + (1 + p + q + pq + qr)

    are added to

    (1 + p + q + pq + qr)(1 + p + pr)

    My answer in the HW was (1 + p + q + pq + qr)(1 + p + pr) but it was missing the extra terms. Can anyone help me understand why step 1 is the product for the if/then but in step two, also an if then, we have 1 + (1 + p + q + pq + qr) in addition to the if/then product.
     
  2. jcsd
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