Question

Three sets of simultaneous equations are given as
$\left(i\right)\overline{A}+AB=0$
$\left(ii\right)\overline{A}+AC=0$
$\left(iii\right)AB+A\overline{C}+CD=\overline{C}D$

The solution of the above three sets of simultaneous equations will be

• A. $A=D=1\text{and}B=C=0$
• B. $B=C=D=1\text{and}A=0$
• C. $C=D=1\text{and}A=B=1$
• D. $A=1\text{and}B=C=D=0$

Answer 1

The correct option is A $A=D=1\text{and}B=C=0$

$\text{Given,}\overline{A}+AB=0$
$\Rightarrow (\overline{A}+A)(\overline{A}+B)=0$
$\Rightarrow \overline{A}+B=0$
$\text{Now}AB=AC$
$\text{or}B=C$
$\text{and}AB+A\overline{C}+CD=\overline{C}D$
$1.0+1.1+0.D=1.D$
$\therefore D=1$
Here option (a) is correct.