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Equation to minimize using Boolean Algebra Laws: $A+\bar{A} B \bar{C}$

I have tried doing this but i am unsure of the answer: $$ \begin{array}{l} \text { Let } K=B \bar{C} \\ A+\bar{A} K=A+K=A+B \bar{C} \end{array} $$

Debanjan Dhar
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2 Answers2

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You can always add a lesser expression as in

$$ A = A + AX $$ Therefore

\begin{align} A + \bar{A}B\bar{C} & = (A + AB\bar{C}) + \bar{A}B\bar{C} \\ & = A + (AB\bar{C} + \bar{A}B\bar{C}) \\ & = A + (A+\bar{A})B\bar{C} \\ & = A + B\bar{C} \end{align}

rewritten
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One more possible way $$A+\overline{A}B\overline{C} =A+B\overline{A+C}=A+ \overline{\overline{B}+A+C}=\\ =\overline{\overline{A}(\overline{B}+A+C)} = \overline{\overline{A}(\overline{B}+C)}=A+B\overline{C}$$

zkutch
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