Question

What will be the input of $A$ & $B$ for the 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 $0,0$

Let the given expression be $X$

$\Rightarrow X=\left(\overline{A+B}\right).\left(\overline{A.B}\right)=1$

Using De-Morgan`s formula, we can simplify the above expression

$\overline{A+B}=\overline{A}.\overline{B}$

$\overline{A.B}=\overline{A}+\overline{B}$

$\Rightarrow X=\overline{A}.\overline{B}(\overline{A}+\overline{B})$

$\Rightarrow X=\overline{A}\overline{B}\overline{A}+\overline{A}\overline{B}\overline{B}$

Using $\overline{A}.\overline{A}=\overline{A}$

$\Rightarrow X=\overline{A}\overline{B}+\overline{A}\overline{B}$

$\Rightarrow X=\overline{A}\overline{B}$

$\therefore$ For $X=1$, then both $\overline{A}$ & $\overline{B}$ should be $1$

$\Rightarrow A=0,B=0$

Hence, option $\left(A\right)$ is correct.

Why this question? Key concept :- Boolean logic follows commutative law & associate law, which is being used in the above question.