What is output of the logic circuit shown below ? 

We can seethe lower input of all the OR gate is same. So lower input all OR gate is X.  

According to given diagram, there area 4 OR gates and in case of OR gate 

1 + X = 1

$\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Y\hspace{0.17em}=1}$