NIELIT 2021 Dec Scientist A - Section B: 52

Question

Which of the following Boolean algebra rules is correct ?

• A. $ A. \overline{\rm A} = 1$
• B. $ A + AB = A + B $
• C. $ A(A+B) = B $
• D. $ A+ \overline{\rm A}B = A + B $

Answer 1

Option $(D)$ is correct here.

1. $A.\bar A=1$ is false. $A.\bar A=0$ is correct.
2.  $A+AB=A+B$ is also false. $A(1+B)\implies A.1=A$
3. $A(A+B)=B$ is false. $(A+AB)$ can be written as option $2$
4. $A+\bar AB=A+B$ is true using distributive law.

$A+\bar AB\implies (A+\bar A)(A+B)\implies (A+B)$