The output of the given circuit diagram is

If $A=0; \overline{A}=1$

$A=1; \overline{A}=0$

$B=0; \overline{B}=1$

$B=1;\overline{ B}=0$

Using De Morgan's theorem, we can write 

$$\begin{gathered} Y=\overline{\left(A+\overline{B}\right)+\left(\overline{A}+B\right)} \\ =\overline{\left(A+\overline{B}\right)}·\overline{\left(\overline{A}+B\right)} \\ =\left(\overline{A}·B\right)·\left(A·\overline{B}\right) \\ =0 \end{gathered}$$