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Math Help - boolean expression

  1. #1
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    boolean expression

    hello, I am trying to understand boolean expressions.
    Can someone please tell me what the following equates to, so I can see how it works.

    not(A) + A.B = ?

    I know that not(A) + A = 1, but how do I finish off this one ?

    thanks kindly.
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  2. #2
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    I assume that A.B is the conjunction ("and") of A and B. I'll skip the period below and will write ~A for not(A).

    ~A + AB can be simplified to ~A + B as follows:

    ~A + AB = ~A(1 + B) + AB = ~A + ~AB + AB = ~A + (~A + A)B = ~A + 1B = ~A + B.

    To come up with this, I drew a Venn diagram of ~A + AB to see that it is ~A + B, then double-checked it using truth tables (without writing everything), and finally decided to represent B in the right-hand side, ~A + B, as (~A + A)B because the left-hand side, ~A + AB, contains AB.
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  3. #3
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    thanks kindly, I understand now.
    Last edited by fran1942; May 14th 2011 at 12:57 PM.
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