The output of the given circuit diagram is

output of this upper OR gate be $$Y_1$$:

$$ Y_1 = A + \overline{B} $$
the output of this lower gate be $$Y_2$$:
$$ Y_2 = \overline{A} + B $$
The final logic gate is a NOR gate
$$ Y = \overline{Y_1 + Y_2} $$
$$ Y = \overline{(A + \overline{B}) + (\overline{A} + B)} $$
$$ Y = \overline{(A + \overline{A}) + (B + \overline{B})} $$
According to Boolean algebra rules, the OR operation between a variable and its complement is always 1
($$A + \overline{A} = 1$$ and $$B + \overline{B} = 1$$):
$$ Y = \overline{1 + 1} $$
$$ Y = \overline{1} $$
$$ Y = 0 $$