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Homework Help: Digital logic - Boolean algebra simplification problem

  1. Feb 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Simplify (A+B')(B+C)

    3. The attempt at a solution
    I first expanded it and got
    = AB + AC + B'B + B'C
    = AB + AC + B'C

    Turns out the solution is AB + B'C (according to an online source). How do we get rid of the AC term?
  2. jcsd
  3. Feb 22, 2014 #2


    User Avatar

    Staff: Mentor

    On examining the expression, you can see ....
    If B is true, then for the expression to be true, the only condition that need be met is that A is true, and it doesn't matter what C is.

    If B is false, then for the expression to be true all we need is that C is true, it doesn't matter what A is.

    Just as in algebra you can multiply any term by 1 and you don't change its value, then in Boolean algebra you can multiply a term by true and you change nothing.

    For example, (B+B') is true, and it's always true.

    AB + AC(B+B') + B'C

    expand this out, then simpify the result
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