Question

Which of the following is not equal to 1 in boolean algebra?

• A. A+1
• B. $A.\bar{A}$
• C. $A+\bar{A}$
• D. $\overline{A.A}$

Answer 1

Answer: (B)

$A.\bar{A}$

Answer 2

The correct option is (B) $A$.$\bar{A}$
Option (a): In boolean algebra, if A=1→$\bar{A}$=0 and A=0→$\bar{A}$=1

Thus, A+1=1
(∵0+1=1 and 1+1=1 in boolean)

Option (b):
if A=1,A.$\bar{A}$=1.0=0
A=0 then A.$\bar{A}$=0.1=0

⇒A.$\bar{A}$=0 always

Option (c): Similarly, A+$\bar{A}$=1 always
Case 1: A=0 ⇒ A+$\bar{A}$=0+1=1

Case 2: A=1⇒A+$\bar{A}$=1+0=1

Option (d):$\overline{A.A}$=$\bar{A}$ (∵A.A=A)

⇒ $\overline{A.A}$=0, if A = 1

⇒ $\overline{A.A}$=1, if A = 0

Hence, option (B) is correct.