A and B are the inputs and Y is the output of the given circuit. The left half of the given figure acts as the NOR Gate, while the right half acts as the NOT Gate. This is shown in the following figure.

Hence the output of the NOR Gate =$\overline{A+B}$

This will be the input for the NOT Gate. Its output will be  \(\overline{\overline{A+B}}=A+B\)$$

$\therefore Y=A+B$

Hene, this circuit functions as an OR Gate. 

(b)
Hint: Identify the truth table for given circuit.
Step: Find the output for the given circuit.
A and B are the inputs and Y is the output of the given circuit. It can be observed from the following figure that the inputs 

of the right half NOR Gate are the outputs of the two NOT Gates.

Hence, the output of the given circuit can be written as:
\(Y=\overline{\bar{A}+\bar{B}}=\overline{\bar{A}} \cdot \overline{\bar{B}}=A \cdot B\\ \text{Hence, this circuit functions as an AND Gate.}\)