The logic circuit shown below is equivalent to:

Output of first OR gate is $A=(X+\bar Y)$ Inputs of second OR gate are $\bar X$ and $\bar Y$. Output of second OR gate is $C = \bar X + \bar A$ $= \bar X+\overline{X+\bar Y} = \bar X+ (\bar X.\overline{\bar Y}) =\bar X+ (\bar X.Y)$ $= \bar X(1+Y) = \bar X$ Final output is $Z =\bar C =\overline{\bar X}+X$