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For the life of me, I can't figure out how to get this into minimal product of sums form. Any help is appreciated.

(a+b+c)(a+b'+c)(a+b'+c')(a'+b'+c')

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    $\begingroup$ The only difference between the first two factors is the $b$ and $b'$. Interpreting as propositional variables, if $b$ is true, the truth of the product of the first two terms is reduced to whether $a+c$ is true. Similarly if $b$ is false. Thus, intuitively, the product of the first two factors should be $a+c$. (A similar thing happens with the last two factors.) This can be verified using the Boolean algebra axioms, specifically distributivity, idempotence, $b+b'=1$, and $bb'= 0$. I don't know if there is a minimization procedure, but what I'm suggesting does reduce the number of factors. $\endgroup$ Sep 19, 2014 at 15:19

1 Answer 1

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This product-of-maxterms expression can be reduced to the following sum of minterms

!bc or a!c

             ab
       00  01  11  10
      +---+---+---+---+
   0  | 0 | 0 | 1 | 1 |
c     +---+---+---+---+
   1  | 1 | 0 | 0 | 1 |
      +---+---+---+---+
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