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# The exercise relates to inhabitants of an | Ch 1.2 - 25E

ISBN: 9780073383095 37

## Solution for problem 25E Chapter 1.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 25E

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 “I am the knave.” and C says “B is the knight.”

Step-by-Step Solution:

Solution:Step 1</p>

In this problem we need to determine who the knave, knight and spy are when is is given that A says “I am the knight.” B says “I am the knave.” and C says “B is the knight.”

It is also given that knights always tell the truth, knaves always lie, and spies who can either lie or tell the truth.

Step 2 of 2

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