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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen
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The exercise relates to inhabitants of an island on which

Chapter 1, Problem 31E

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QUESTION:

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.”

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QUESTION:

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.”

ANSWER:

Solution:

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

Is it possible?

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