In the following circuit, the correct relation between output ($$Y$$) and inputs $$A$$ and $$B$$ will be

To determine the logic operation of the given circuit, we analyze the behavior of the diodes and the NPN transistor for different input combinations:

1. Analysis of the Diode Section (Inputs A and B)

The first part of the circuit (diodes $$D_1$$ and $$D_2$$ connected to a $$-10\text{ V}$$ source through resistor R) acts as an AND gate logic for the point X:

• If either A or B is Low ($$0\text{ V}$$): The corresponding diode becomes forward-biased by the $$-10\text{ V}$$ supply. Point X remains at a low potential.
• If both A and B are High ($$5\text{ V}$$): Both diodes are reverse-biased. Point X rises to a high potential.

2. Analysis of the Transistor Section (Output Y)

The NPN transistor acts as a NOT gate (inverter):

• When X is Low: The transistor is in cutoff. No current flows through $$R_C$$, so the output Y is pulled up to $$5\text{ V}$$ (High).
• When X is High: The transistor goes into saturation. Point Y is shorted to ground, making the output (Low).

3. Truth Table

Conclusion

The output Y is the inverse of the AND operation of the inputs. This corresponds to a NAND gate.

Correct Relation:

$$\boxed{Y = \overline{AB}}$$

Correct Option: (C)