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Need help on how to simplify $[(ABC)' + (B' + C)']'$.

Here is my attempt:

\begin{eqnarray} &&[(ABC)' + (B' + C)']'\\ &=&(ABC) + (B' + C)\\ &=&B'+C(AB + 1)\\ &=&B' + ABC \end{eqnarray}

Is this correct? What can I do next?

Chuks
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eeempoyyy
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1 Answers1

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You didn't apply DeMorgan's Law correctly; you must flip the $+$ to a $\times$ (using concatenation). You should obtain: $$ \begin{eqnarray} [(ABC)' + (B' + C)']' &=&(ABC)''(B' + C)''\\ &=&(ABC)(B' + C)\\ &=&(ABC)B' + (ABC)C\\ &=&A(BB')C + AB(CC)\\ &=&A(0)C + AB(C)\\ &=&0 + ABC\\ &=&ABC\\ \end{eqnarray} $$

Adriano
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