Problem 5 An explorer is captured by a group of cannibals. There are two types o

Question

Problem 5 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 tunless he can determine whether a particular cannihal always lies or always tells the trith. He is allowcd to ask the cannibal cxactly one question. . Explain why the question "Are you a liar?" does not work. . Find a question that the explorer can use to determine whether the cannibal always lies or always tells the truth. Show all your work. Be as brief and as concise as possible. Your answer

Explanation / Answer

1. The question 'are you a liar?' won't work because of the following reasons:

Suppose the explorer asks this question to the one who always lie so, he will 'NO'. And if the explorer asks the same question, he will also say 'NO'. Since, both of them answers the same, it will be pretty difficult to find out which one is lying and which one is telling the truth.

2. But if the explorer asks the original question by modifying it like ‘If I were to ask are you a liar, would you answer yes?’, the one who always tell truth will say ‘YES’. But the one who always lie will answer ‘NO’. The reason for ‘NO’ as the liar will make two negations. So, based on the answer given by the cannibal, the explorer can easily find out who’s who.

So, the question he should ask is If I were to ask are you a liar, would you answer yes? If cannibal says ‘YES’ then he is the one who always tell truth. If cannibal says ‘NO’ then he is the one who always lie.

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