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 $Z =\bar C =\overline{\bar X}+X$