Answer to Question #131569 in Discrete Mathematics for sudhanshu kumar

Question

An explorer is captured by a group of cannibals. There are two types of cannibals: those who always tell the truth and those who always lie. The cannibals will barbecue the explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He is allowed to ask the cannibal exactly one question.
(a) Explain why the question “Are you a liar?” does not work.
(b) Find a question that the explorer can use to determine whether the cannibal always lies or always tells the truth.

Answer 1

1. The question, 'Are you a liar' does not work because, if the canibal always lies, he will answer NO because he will be lying. If the canibal always tells the truth, then his answer will also be NO because he will be telling the truth that he is not a liar. Therefore it will be impossible to distinguish the liar from the one who always tells the truth based on that question.
2. Any tautology question would work, for instance, the explorer could ask the canibals, 'Are you a canibal?' The one who always lies will answer by saying NO and the one who always tells the truth will answer by saying YES.