$$ \begin{aligned} Y_1 \& =\overline{A \cdot A} \\ \& =\bar{A} \\ Y_2 \& =\overline{B+B} \\ \& =\bar{B} \\ Y \& =\overline{Y_1+Y_2} \\ \& =\overline{\bar{A}+\bar{B}} \\ \& =\overline{\bar{A}} \cdot \overline{\bar{B}} \end{aligned} $$

= A.B is similar to output of AND gate.