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# An explorer is captured by a group of cannibals. There are

ISBN: 9780073383095 37

## Solution for problem 16E Chapter 1.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 16E

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.

Step-by-Step Solution:

Step 1 :

The objective of this question is to judge the person is the liar or tell the truth. 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.

Step 2 :

a). Explain why the question “Are you a liar?” does not work.

Here, we have followed all the conditions, according to the question, then we can distinguish the liar person or truth teller person. In the first case, if the explorer asks the question to the liar, “ Are you liar “, Liar say “NO”, as per his nature.

If the same question asked by the explorer to the truth teller person “Are you liar “, so he would say “NO”, in both the cases liar and non-liar says “NO”, So, here is very difficult to distinguish them. That is why that question doesn’t work.

Step 3 of 3

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