Both diodes are assumed to be ideal. The current source has I Amp current through it .I am not sure about the voltages at the cathode of diodes and thus I am confused when the diodes will be turned ON and OFF. So How we can decide that when the voltage at A and B is Low then both diodes are OFF because it might be case that voltage at cathode is much Lower or negative than anode.I mean how we decide that diodes are ON or OFF when we know the anode voltage only
This seems to be a classic Diode-OR Gate. Both diodes are forward biased, therefore they both serve as a conductive path to Y so long as the input exceeds the Vf of the Diodes. So if Diode A OR Diode B are conducting, A voltage will be present at Y. General Description of Diode Transistor Logic "DTL"
I assume there's 1N4148 only because the schematic editor insisted that something from the component list must be selected. The question text states the diodes to be ideal.
This question really can't be answered shortly before we have an agreement on what measurables define the logic states and how. An example:
Let the states be defined by the node voltages against GND. Let 0V be the treshold between the states True and False. If positive voltage mean True, then this is OR. If negative voltage means True, this is AND.