NIELIT 2021 Dec Scientist B - Section B: 94

Question

The complement of the expression $Y = ABC + AB \overline{\rm C} + \overline{\rm A}\; \overline {\rm B} C + \overline{\rm A} BC$ is $:$

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

Answer 1

To find the complement of any boolean expression following steps are there:

1. Convert $0$ to $1$ and vice versa.
2. Convert $+$ to $*$ and vice versa
3. Take variables complement, $A\leftrightharpoons \bar A$ 

So complement of the given expression is as follow:

$Y=ABC+AB\bar C+\bar A\bar BC+\bar ABC$

$Y=AB(C+\bar C)+\bar AC(\bar B+B)$

$Y=AB+\bar AC$

$Y^c=(\bar A+\bar B)*(A+\bar C)$

Option $(A)$ is correct.