(a)
Hint: Identify the truth table for a given circuit.
Step 1: Find the output for the given circuit.
A act as the two inputs of the NOR gate and Y is the output, as shown in the following figure. Hence, the output of the circuit is \(\overline{A+A}.\)
  
Step 2: Draw the truth table.
The truth table for the same is given as:

A	Y(=\(\overline{A}\))
0	1
1	0

This is the truth table of a NOT gate. Hence, this circuit functions as a NOT gate.

(b)
Hint: Identify the truth table for a given circuit.
Step 1: Find the output for the given circuit.
A and B are the inputs and Y is the output of the given circuit. By using the result obtained in solution (a), we can infer that the outputs of the first two NOR gates are \(\bar{A}\) and \(\bar{B}\)  as shown in the following figure.
     
\(\overline{\mathrm{A}}~ and ~\overline{\mathrm{B}}\) are the inputs for the last NOR gate. Hence, the output for the circuit can be written as:
\(Y=\overline{\overline{\mathrm{A}}+\overline{\mathrm{B}}}=\overline{\overline{\mathrm{A}}} \cdot \overline{\overline{\mathrm{B}}}=A \cdot B\)
Step 2: Draw the truth table.
The truth table for the same can be written as:

A	B	Y(=A·B)
0	0	0
0	1	0
1	0	0

This is the truth table of an AND gate. Hence, this circuit functions as an AND gate.