Hi Abbas,
Here's the explanation.........
Let's the Two doors be x and y........
X is Life door and Y is Death door.............
Case 1) Guard A is the one who tells Truth :-
In this case the Prisoner asks "Which Door wud the other Guard ask me to take to save my Life?". Since the man tells the truth, he would know that Guard B would misguide the traveller by lying......
he would answer by saying that "He would ask you to take path Y"........
so if the Prisoner assumes that the Guard A says the truth, he would know that the other Guard would lie so he is left wid only path X"
Case 2) The Guard A is the one who lies :-
If the same ques i.e. "Which path wud the other Guard ask me to take to get to the city?"
is asked to the liar he would reply " Guard B wud ask u to take path Y".
now this is a lie...
So if the Prisoner assumes that the Guard A is a liar, he wud know that he wud give a false statement about the other Guard.....so the correct path is path X
Based on both assumptions, irrespective of the Guard telling a truth or a lie.......the answer remains the same......!!!!
Phew... Is that right Abbas??