The output of the given logic circuit is

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(C) The given circuit consists of two $OR$ gates followed by an $AND$ gate.$1$. The inputs to the first $OR$ gate are $A$ and $B$. Therefore,its outpu

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$(A+B) \cdot(A+C)$

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(C) The given circuit consists of two $OR$ gates followed by an $AND$ gate.$1$. The inputs to the first $OR$ gate are $A$ and $B$. Therefore,its output is $(A+B)$.$2$. The inputs to the second $OR$ gate are $A$ and $C$. Therefore,its output is $(A+C)$.$3$. These two outputs $(A+B)$ and $(A+C)$ are fed as inputs to the final $AND$ gate.$4$. The output $Y$ of the $AND$ gate is the product of its inputs: $Y = (A+B) \cdot (A+C)$.

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