Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.3 - Page 63: 38

Answer

A : knave B : knight.

Work Step by Step

Method: Reductio Ad Absurdum (Proof by contradiction) Hypothesis: Let us suppose, on the contrary, that A is a knight. Thus, A spoke the truth and hence A and B are both knights(That's what A said). Thus B also spoke the truth (being a knight) which means A is a knave (that;s what B said). So, we have encountered a contradiction due to our faulty hypothesis. Hence, A is not a knight but is a knave which means B is a knight as he spoke truth
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