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Boolean Algebra Help

  1. Sep 13, 2010 #1
    1. The problem statement, all variables and given/known data
    Simplify the following expressions using Boolean Algebra.

    a) A + AB (A or A and B)
    b) A'BC + AC (A(not) and B and C or A and C)
    c) A'B + ABC' + ABC (A(not) and B or A and B and C(not) or A and B and C)

    2. Relevant equations
    Some simple boolean algebra rules.

    3. The attempt at a solution

    For a, I got the answer of A.
    I did:
    A(1 + B)
    = A

    For b, I got the answer AC.

    I did:
    C(A'B + A)
    C(0 + A)
    = AC

    For c, I got the answer AB.
    I did:
    B(A' + AC' + AC)
    B(A' + (A.C') + (A.C))
    B(A' + (0) + A)
    B(A' + A)
    = AB

    Are my calculations correct or am I completely wrong? Thank you for your help.
  2. jcsd
  3. Sep 13, 2010 #2


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    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Looks good.
    How did you replace A'B with 0?
    It's not clear what you did from the second to third line, and you simplified A'+A incorrectly.
    When you have only a few variables, it's easy enough to verify that you simplified an expression correctly by writing out the truth table. For example, for A'BC+AC, you get
    Code (Text):
    A B C   A'  A'BC   AC    A'BC+AC
    T T T   F     F     T       T
    T T F   F     F     F       F
    T F T   F     F     T       T
    T F F   F     F     F       F
    F T T   T     T     F       T
    F T F   T     F     F       F
    F F T   T     F     F       F
    F F F   T     F     F       F
    Comparing the columns for AC and A'BC+AC, you can see they're not equal, so you know something went wrong in the simplification.
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