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(C) The given circuit consists of a $NAND$ gate and a $NOT$ gate,whose outputs are fed into an $OR$ gate.$1$. The inputs $A$ and $B$ are fed into a $N

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

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(C) The given circuit consists of a $NAND$ gate and a $NOT$ gate,whose outputs are fed into an $OR$ gate.$1$. The inputs $A$ and $B$ are fed into a $NAND$ gate. The output of the $NAND$ gate is $\overline{A \cdot B}$.$2$. The input $C$ is fed into a $NOT$ gate. The output of the $NOT$ gate is $\overline{C}$.$3$. These two outputs are then fed into an $OR$ gate. The $OR$ operation of two inputs $X$ and $Z$ is $X+Z$.$4$. Therefore,the final output $Y$ is the $OR$ sum of the two previous outputs: $Y = \overline{A \cdot B} + \overline{C}$.

In the digital circuit,the inputs are as shown in the figure. The Boolean expression for output $Y$ is

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