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What will be the input of $A$ and $B$ for the Boolean expression $\overline{(A+B)} \cdot \overline{(A \cdot B)}=1$
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Verified Answer
The correct answer is:
0,0
The given Boolean expression can be written as
$\begin{aligned}
& Y=(\overline{A+B}) \cdot(\overline{A \cdot B})=(\bar{A} \cdot \bar{B}) \cdot(\bar{A}+\bar{B})=(\bar{A} \cdot \bar{A}) \cdot \bar{B}+\bar{A}(\bar{B} \cdot \bar{B}) \\
& =\bar{A} \cdot \bar{B}+\bar{A} \bar{B}=\bar{A} \bar{B}
\end{aligned}$
$\begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 1 \\ \hline 1 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 1 & 0 \\ \hline \end{array}$
$\begin{aligned}
& Y=(\overline{A+B}) \cdot(\overline{A \cdot B})=(\bar{A} \cdot \bar{B}) \cdot(\bar{A}+\bar{B})=(\bar{A} \cdot \bar{A}) \cdot \bar{B}+\bar{A}(\bar{B} \cdot \bar{B}) \\
& =\bar{A} \cdot \bar{B}+\bar{A} \bar{B}=\bar{A} \bar{B}
\end{aligned}$
$\begin{array}{|c|c|c|} \hline A & B & Y \\ \hline 0 & 0 & 1 \\ \hline 1 & 0 & 0 \\ \hline 0 & 1 & 0 \\ \hline 1 & 1 & 0 \\ \hline \end{array}$
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