Output of following logic circuit is

In the given circuit, the outputs of all three $OR$ gates is given to the input of $AND$ gate.

Inputs to the first $OR$ gate are $\overline{A}$ and $B$ as a $NOT$ gate in between the input from $A$. Similarly, inputs to second $OR$ gate are $\overline{A}$ and $\overline{C}$. And to third $OR$, inputs are $B$ and $\overline{C}$. 

We know the output of an $OR$ gate is the sum of inputs. Then, the outputs of the three $OR$ gates are $\left(\overline{A}+B\right)$, $\left(\overline{A}+\overline{C}\right)$ and $\left(B+\overline{C}\right)$.

Now, we know that the output of the $AND$ gate is the multiplication of the inputs. Therefore, the output of logic circuit is $Y=\left(\overline{A}+B\right)·\left(\overline{A}+\overline{C}\right)·\left(B+\overline{C}\right)$.