Question

In Boolean algebra $\overline{(A+\overline{B})\cdot C}$ will be equal to.

• A. $(\overline{A}\cdot B)+\overline{C}$
• B. $(A\cdot \overline{B})+C$
• C. $(A\cdot B)\cdot C$
• D. $(A+\overline{B})+C$

Answer 1

The correct option is A $(\overline{A}\cdot B)+\overline{C}$

$\overline{(A+\overline{B})\cdot C}=\overline{(A+\overline{B})}+\overline{C}$
(From De Morgan's theorem)
$=(\overline{A}\cdot \overline{B})+\overline{C}$ (From De Morgan's theorem)
$=(\overline{A}\cdot B)+\overline{C}$.