Write the truth table for the circuits given in figure. Considering of NOR gate only. Identify the logic operations (OR, AND, NOT) performed by the two circuits.

Hint: In the above solved question, we have used Boolean operations for some basic logic gates such as OR, AND, NOT gates. We drew truth tables for the combinations of basic logic gates, which represents their functions for all combinations of input signals.

Complete step-by-step answer:
Logic gates are important digital devices that are mainly based on the Boolean functions. Logic gates take one or more binary (0 or 1) input signal, and carry out logical operations on them and give one binary (0 or 1) output.
Boolean operations for several basic gates-
1. For OR gate: $Y = X + Y$
2. For AND gate: $Y = X·Y$.
3. For NOT gate: $Y=\overline{X}$
Now using the above described Boolean functions, we can make truth tables for the figures mentioned in the question.

1. Truth table for diagram (a)-
It is a NOR gate, which has both input A and output Y.
So, the operation will be $Y=\overline{A}$.
As, $Y=\overline{X+Y}=\overline{A+A}=\overline{A}$

2. Truth table for diagram (b)-
It is a three NOR gates circuit, it’s output will be $Y=\overline{\overline{A}+\overline{B}}$

If you observe carefully, this gate essentially is an AND gate.

Note: According to their mode of operations, logic gates have a lot of applications.
Logic gates are usually found in circuits such as safety thermostat, push-button lock, automatic watering system, light activated burglar alarm system.
Logic gates can be found in IC circuits.