Which of the following circuits has the same outpur as that of the given circuit?

• A

  
  
• Correct answer
  B

  
  
• C

  
  
• D

  
  

Solution

$\begin{aligned} & \mathrm{P}=\mathrm{A} \cdot \overline{\mathrm{B}} \\ & \mathrm{Q}=\mathrm{A} \cdot \mathrm{B} \\ & \mathrm{Y}=\overline{\mathrm{P}+\mathrm{Q}}=\overline{\mathrm{A} \cdot \overline{\mathrm{B}}+\mathrm{A} \cdot \mathrm{B}} \\ & =\overline{\mathrm{A} \cdot(\mathrm{B}+\overline{\mathrm{B}})}=\overline{\mathrm{A} \cdot \mathrm{I}} \\ & \mathrm{Y}=\overline{\mathrm{A}}\end{aligned}$

Hence, the correct answer is option: 'B'.