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(C) The given digital circuit consists of a $NAND$ gate and a $NOT$ gate,whose outputs are fed into an $OR$ gate.$1$. The output of the $NAND$ gate wi

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$\bar{A}+\bar{B}+\bar{C}$

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(C) The given digital circuit consists of a $NAND$ gate and a $NOT$ gate,whose outputs are fed into an $OR$ gate.$1$. The output of the $NAND$ gate with inputs $A$ and $B$ is $\overline{AB}$.$2$. The output of the $NOT$ gate with input $C$ is $\bar{C}$.$3$. These two outputs are fed into an $OR$ gate,so the final output $Y$ is $Y = \overline{AB} + \bar{C}$.$4$. According to De Morgan's theorem,$\overline{AB} = \bar{A} + \bar{B}$.$5$. Substituting this into the expression for $Y$,we get $Y = \bar{A} + \bar{B} + \bar{C}$.

The inputs to the digital circuit are as shown below. The output $Y$ is

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