Question

The input of $A$ and $B$ for the Boolean expression $\left(\overline{A+B}\right).\left(\overline{A.B}\right)=1$ is

• A. $0,0$
• B. $0,1$
• C. $1,0$
• D. $1,1$

Answer 1

The correct option is A $0,0$

Given equation is: $\left(\overline{A+B}\right)\left(\overline{A.B}\right)$
A] For $(0,0)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(\overline{0+0}\right)\left(\overline{0.0}\right)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(1\right)\left(1\right)=1$

B] For $(0,1)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(\overline{0+1}\right)\left(\overline{0.1}\right)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(0\right)\left(1\right)=0$

C] For $(1,0)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(\overline{1+0}\right)\left(\overline{1.0}\right)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(0\right)\left(1\right)=0$

D] For $(1,1)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(\overline{1+1}\right)\left(\overline{1.1}\right)$
$\left(\overline{A+B}\right)\left(\overline{A.B}\right)=\left(0\right)\left(0\right)=0$