Question

The logic expression which is not equal to $1$ in Boolean algebra is

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

Answer 1

Answer: (B), (D)

$A.\overline{A}$
$\overline{\overline{A+A}}$

$A+1$ is addition of $1$ to value of $A$, which can be any of $0$ and $1$. This expression would always given '$1$' as the output since addition of $1$ to anything gives $1$.

$A.\overline{A}$ gives $0$ always because whatever value $A$ assumes, $\overline{A}$ assumes the other and they give $0$ under AND operation.

$A+\overline{A}$ would always give value $1$ because whatever value $A$ assumes, $\overline{A}$ assumes the other and they give $1$ under OR operation.

$\overline{\overline{A.A}}=A.A=A$ which is might be $1$ for value of $A=1$.