The output Y of following circuit for given inputs is :

Inputs entering the top OR gate:

$$\text{Top input} = A$$

$$\text{Bottom input} = \bar{B} \quad (\text{via NOT gate})$$

$$\text{Output of OR gate} = A + \bar{B}$$

Inputs entering the bottom AND gate:

$$\text{Top input} = B$$

$$\text{Bottom input} = \bar{A} \quad (\text{via NOT gate})$$

$$\text{Output of bottom AND gate} = \bar{A} \cdot B$$

Output $$Y$$ from the final AND gate: $$Y = (A + \bar{B}) \cdot (\bar{A} \cdot B)$$

$$Y = A \cdot (\bar{A} \cdot B) + \bar{B} \cdot (\bar{A} \cdot B)$$ $$\implies Y = (A \cdot \bar{A}) \cdot B + \bar{A} \cdot (B \cdot \bar{B})$$

$$Y = 0 \cdot B + \bar{A} \cdot 0 \implies Y = 0$$