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Solved: The exercise relates to inhabitants of an island

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 28E Chapter 1.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 28E

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 the knight,” B says. “A is not the knave.” and C says “B is not the knave.”

Step-by-Step Solution:
Step 1 of 3

Solution: Step-1: In this problem we need to determine who the knave , knight and spy are . Given : A says that “ I am the knight ” , B says “ A is not the knave ” and C says “ B is not the knave ”. Also given that Knight who always tell the truth , knaves who always lie , and spies who can either lie or tell the truth.Step-2: ABCTruth values of the statement Is it possibleKnight Knave SpyA(t)B(t)C(f)Knight SpyKnaveA(t)B(t)C(t)SpyKnight Knave A(f)B(t)C(t)SpyKnave KnightA(f)B(t)C(f)KnaveSpy Knight A(f)B(f)C(t)yesKnaveKnightSpyA(f)B(f)C(f) Therefore , only option is C is the knight , B is the spy , and A must be the knave.

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Chapter 1.2, Problem 28E is Solved
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Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Solved: The exercise relates to inhabitants of an island