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Math Help - Boolean Expression

  1. #1
    WWU
    WWU is offline
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    Boolean Expression

    Hello,

    Ok so I have the following equation: A'B'C + A'BC + AB'C + ABC' + ABC

    I know that the most simplified form is AB + C but I cannot arrive at that solution.
    Every time I try to work it out the first thing I do is Simplify the last two terms as follows: AB(C' + C) = AB

    So the new equation is: A'B'C + A'BC + AB'C + AB

    Now I tried removing C and getting the following: C(A'B' + A'B + AB') + AB

    From here I am stuck and I have tried to solve it many other ways but always get stuck or eliminate something I don't want to. Help would be much appreciated
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  2. #2
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    A'B'C + A'BC + AB'C + ABC' + ABC

    = A'B'C + A'BC + AB'C + ABC + ABC'
    = C + ABC'
    Let AB = X, then we have
    C + XC'
    = C(X+X') + XC'
    = C(X + X' + X) + XC'
    = C(X + X') + X(C+C')
    = C + X
    = C + AB
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  3. #3
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    The problem is that the expression by which C is multiplied, i.e., A'B' + A'B + AB' is not a tautology. We can turn it into one by adding a second copy of ABC to the original expression. The expression is then broken into two parts: ABC + ABC' = AB and A'B'C + A'BC + AB'C + ABC = C(A'B' + A'B + AB' + AB) = C.

    By the way, the original formula is not an equation; an equation must have an = sign.
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