Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.2 - Applications of Propositional Logic - Exercises - Page 23: 21

Answer

Either Person A is a knight and Person B is a knave, or Person A is a knave and Person B is a knight.

Work Step by Step

Person A says "I am a knave or person B is a knight" and person B says nothing. Person B's silence gives no information as to whether she is a knight or knave. If person A is a knave, the first half of the statement is true so the second half must be a lie. Thus, person B is a knave as well. If person A is a knight, the first half of the statement is untrue so the second half must be true. Thus, person A can be a knight if person B is a knave.
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