Question

The following is NOT equal to $0$ in the Boolean algebra is

• A. $\overline{\overline{A}.0}$
• B. $A.\overline{A}$
• C. $A.0$
• D. $\overline{A+\overline{A}}$

Answer 1

Answer: (A)

(A) For $A=0$,
$\overline{\overline{A}.A}=\overline{\overline{0}.0}=\overline{1.0}=\overline{0}=1$
For $A=1$,
$\overline{\overline{A}.A}=\overline{\overline{1}.1}=\overline{0.1}=\overline{0}=1$

(B) For $A=0$,
$A.\overline{A}=0.\overline{0}=0.1=0$
For $A=1$,
$A.\overline{A}=1.\overline{1}=1.0=0$

(C) For $A=0$,
$A.0=0.0=0$
For $A=1$,
$A.0=1.0=0$

(D) For $A=0$,
$\overline{A+\overline{A}}=\overline{0+\overline{0}}=\overline{0+1}=\overline{1}=0$
For $A=1$,
$\overline{A+\overline{A}}=\overline{1+\overline{1}}=\overline{1+0}=\overline{1}=0$