Q. What will be the input of $A$ and $B$ for the Boolean expression $\overline{(A + B)} \bullet \overline{(A \bullet B)} = 1$
A) 0, 0
B) 0, 1
C) 1, 0
D) 1, 1
Explanation
(a) The given Boolean expression can be written as
$Y = \left( \overline{A + B} \right).\left( \overline{A.B} \right) = \left( \overline{A}.\overline{B} \right).\left( \overline{A} + \overline{B} \right) = \left( \overline{A}\ \overline{A} \right).\overline{B} + (\overline{B}.\overline{B})$
$= \overline{A}.\overline{B} + \overline{A}\ \overline{B} = \overline{A}\ \overline{B}$
[table] $\mathbf{A}$ | $\mathbf{B}$ | $\mathbf{Y}$ ; 0 | 0 | 1 ; 1 | 0 | 0 ; 0 | 1 | 0 ; 1 | 1 | 0 [/table]
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.