Question

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

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

Answer 1

The correct option is B $A.\overline{A}$

Option $\left(a\right):$ In boolean algebra, if $A=1\to \overline{A}=0\text{and}A=0\to \overline{A}=1$

Thus, $A+1=1$
$(\because 0+1=1\text{and}1+1=1\text{in boolean})$

Option $\left(b\right)$:
if $A=1,A.\overline{A}=1.0=0$
$A=0\text{then}A.\overline{A}=0.1=0$

$\Rightarrow A.\overline{A}=0$ always

Option $\left(c\right)$: Similarly, $A+\overline{A}=1$ always
Case 1: $A=0\Rightarrow A+\overline{A}=0+1=1$

Case 2: $A=1\Rightarrow A+\overline{A}=1+0=1$

Option $\left(d\right)$: $\overline{A.A}=\overline{A}(\because A.A=A)$

$\Rightarrow \overline{A.A}=0,\text{if A = 1}$

$\Rightarrow \overline{A.A}=1,\text{if A = 0}$

Hence, option $\left(B\right)$ is correct.