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# Solution: The exercise relates to inhabitants of an island

ISBN: 9780073383095 37

## Solution for problem 30E Chapter 1.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition

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Problem 30E

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 “A is the spy.”

Step-by-Step Solution:
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Solution:Step1Given 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.Step2To findWe 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.Step3We haveA saying “I am not the spy,” B saying “I am not the spy,” and C saying “A is the spy.”ABCTruth values of the given statementIs it possibleSpyKnaveKnightA(F).B(T),C(T)KnaveKnightSpyA(T),B(F),C(F)KnightSpyKnaveA(T),B(F),C(F)yesSpyKnightKnaveA(F),B(T),C(T)KnaveSpyKnightA(T),B(F),C(F)KnightKnaveSpyA(T),B(T),C(F)Therefore, the only possibility is A is Knight, B is the Spy, and C must be the Knave.

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Solution: The exercise relates to inhabitants of an island