Question

What will be the input of A and B for Boolean expression $\left(\overline{A+B}\right)\left(\overline{A.B}\right)=1$?

• A. 0,0
• B. 0,1
• C. 1,0
• D. 1,1

Answer 1

The correct option is A

0,0

The explanation for the correct result:

Option A:

$\begin{array}{rcl}A& =& 0\\ B& =& 0\end{array}$

Now,

$\begin{array}{rcl}\left(\overline{\mathrm{A}+\mathrm{B}}\right)\left(\overline{\mathrm{A}.\mathrm{B}}\right)& =& \left(\overline{0+0}\right)\left(\overline{0.0}\right)\\ & =& \left(\overline{0}\right)\left(\overline{0}\right)\\ & =& \left(1\right)\left(1\right)\\ & =& 1\end{array}$

The explanation for the incorrect result:

Option B:

$$\begin{gathered} A=0 \\ B=1 \end{gathered}$$

So,

$\begin{array}{rcl}\left(\overline{\mathrm{A}+\mathrm{B}}\right)\left(\overline{\mathrm{A}.\mathrm{B}}\right)& =& \left(\overline{0+1}\right)\left(\overline{0.1}\right)\\ & =& \left(0\right)\left(1\right)\\ & =& 0\end{array}$

Option C:

$$\begin{gathered} A=1 \\ B=0 \end{gathered}$$

So,

$\begin{array}{rcl}\left(\overline{\mathrm{A}+\mathrm{B}}\right)\left(\overline{\mathrm{A}.\mathrm{B}}\right)& =& \left(\overline{1+0}\right)\left(\overline{1.0}\right)\\ & =& \left(0\right)\left(1\right)\\ & =& 0\end{array}$

Option D:

$$\begin{gathered} A=1 \\ B=1 \end{gathered}$$

So,

$\begin{array}{rcl}\left(\overline{\mathrm{A}+\mathrm{B}}\right)\left(\overline{\mathrm{A}.\mathrm{B}}\right)& =& \left(\overline{1+1}\right)\left(\overline{1.1}\right)\\ & =& \left(0\right)\left(0\right)\\ & =& 0\end{array}$

Hence, option A is the correct answer.