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# The exercise relates to inhabitants of an island on which

ISBN: 9780073383095 37

## Solution for problem 31E Chapter 1.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 31E

The exercise relates to inhabitants of an island on which there are three kinds of people: Knights who always tell the truth, knaves who always lie, and spies (called normals by Smullyan [Sm78]) who can either lie or tell the truth. You encounter three people A, B, and C. You know one of these people is a knight, one is a knave and one is a spy. Each of these three people knows the type of person each of other two is. For each of those situations, if possible, determine whether there is a unique solution and determine who the knave, knight and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.

A says “I am not the spy.” B says “I am not the spy.” and C says “I am not the spy.”

Step-by-Step Solution:
Step 1 of 3

Step1

Given that

There are three kinds of people in an island on which  Knights who always tell the truth, knaves who always lie, and spies  who can either lie or tell the truth. Three people are A, B, and C. we know one of these people is a knight, one is a knave and one is a spy. Each of these three people knows the type of person each of other two is.

Step2

To find

We have to  determine whether there is a unique solution and  who the knave, knight and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.

Step3

We have

A saying “I am not the spy.” B saying “I am not the spy.” and C saying “I am not the spy.”

...
 A B C Truth values of the given  statement
Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “The exercise relates to inhabitants of an island on which there are three kinds of people: Knights who always tell the truth, knaves who always lie, and spies (called normals by Smullyan [Sm78]) who can either lie or tell the truth. You encounter three people A, B, and C. You know one of these people is a knight, one is a knave and one is a spy. Each of these three people knows the type of person each of other two is. For each of those situations, if possible, determine whether there is a unique solution and determine who the knave, knight and spy are. When there is no unique solution, list all possible solutions or state that there are no solutions.A says “I am not the spy.” B says “I am not the spy.” and C says “I am not the spy.”” is broken down into a number of easy to follow steps, and 143 words. Since the solution to 31E from 1.2 chapter was answered, more than 254 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 31E from chapter: 1.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: spy. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095.

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