The output of the following logic circuit is:

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(C) In the given circuit,the outputs of all three $OR$ gates are fed into the input of an $AND$ gate.Inputs to the first $OR$ gate are $\bar{A}$ and $

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$(\bar{A}+B) \cdot (\bar{A}+\bar{C}) \cdot (B+\bar{C})$

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(C) In the given circuit,the outputs of all three $OR$ gates are fed into the input of an $AND$ gate.Inputs to the first $OR$ gate are $\bar{A}$ and $B$ because there is a $NOT$ gate on the input line from $A$. Thus,the output of the first $OR$ gate is $(\bar{A}+B)$.Inputs to the second $OR$ gate are $\bar{A}$ and $\bar{C}$ because there are $NOT$ gates on both input lines from $A$ and $C$. Thus,the output of the second $OR$ gate is $(\bar{A}+\bar{C})$.Inputs to the third $OR$ gate are $B$ and $\bar{C}$ because there is a $NOT$ gate on the input line from $C$. Thus,the output of the third $OR$ gate is $(B+\bar{C})$.Since the output of an $AND$ gate is the product (logical multiplication) of its inputs,the final output $Y$ of the logic circuit is the product of the outputs of the three $OR$ gates:$Y = (\bar{A}+B) \cdot (\bar{A}+\bar{C}) \cdot (B+\bar{C})$.

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