For the logic gates shown below, the correct output is

• A

  $A+B+C$
• B

  $\bar{A} \cdot \bar{B} \cdot \bar{C}$
• Correct answer
  C

  $\bar{A}+\bar{B}+\bar{C}$
• D

  $\overline{A \cdot B}+\overline{B \cdot C}$

Solution

For the logic gates shown below
The logic operation can be written as $$ \begin{aligned} & \overline{A \cdot A}+(\overline{A \cdot B}+\overline{B \cdot C}+\overline{B \cdot B} \\ & =\overline{A \cdot A}+\bar{A}+\bar{B}+\bar{B}+C+\overline{B \cdot B} \quad(\text { Note } \overline{A \cdot A}=\bar{A}) \\ & =\bar{A}+\bar{A}+\bar{A}+\bar{B}+\bar{B}+\bar{C}+\bar{B} \quad(\text { Note } \bar{A}+\bar{A}=\bar{A}) \\ & =\bar{A}+\bar{B}+\bar{C} \end{aligned} $$

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