a prisoner told if you tell lie we will hang you if you tell the truth we will shoot you
Answers
Answer:
Consider the case where the prisoner says: “You will hang me.”
If the prisoner were to hang, that statement would be true. But if the prisoner speaks a truth, he should be shot, not hanged.
If the prisoner were to be shot, and not hanged, that would be false, in that case the prisoner should have been hanged, not shot.
As written, there is still a way out for the authorities, as there is nothing in the statements above forbidding them from BOTH hanging him AND shooting him, whether he tells a truth or not. Because by hanging him they make the statement true, so they should also shoot him, because that is the punishment for being truthful.
Now consider if the prisoner says: “You won’t shoot me… unless you don’t hang me.”
Likely the authorities will still both hang AND shoot him anyways for making them so confused. They will risk being sanctioned by an appeals court later if the court can figure out what they should have done. Executed prisoners rarely have access to justice after the fact.