GATE IN 2025 | Question: 19

Question

A Boolean function $X$ is given as $X=\bar{A} \bar{B}+\bar{A} \bar{C}$. The reduced form of $\bar{X}$ is

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

Answer 1

X'=((A'B')+(A'C'))'

X'=((A'B'))'.((A'C'))'     {Apply Demorgans Law}

X'=((A')')+((B')').((A')')+((C')')   {Apply Demorgans Law}

X'=(A+B).(A+C)           {((y)')'=y}

X'=(AA+AC+BA+BC)   

X'=A+AC+BA+BC        {y.y=y}

X'=A(1+C+B)+BC        {1+something}=1 

X'=A+BC         

Therefore, Option:B  is correct