Discrete Mathematics with Applications 4th Edition

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

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.4 - Page 143: 27

Answer

Valid. The major and minor premises are diagrammed. There is only one way to compose the diagrams which is also diagrammed. Given true premises, the conclusion is always true. Hence the argument is valid.

Work Step by Step

Alternatively, the argument is true by universal modus tollens. The statement, "Nothing intelligible ever puzzles me" can be rewritten as: "$\forall x$, x is intelligible, then x does not puzzle me." Universal modus tollens: $\forall x, $ if $P(x)$ then $Q(x)$. ~$Q(a)$ for a particular $a$. ~$\therefore P(a)$. In this case P(x) is: x is intelligible. Q(x) is: x does not puzzle me. a is logic. ~Q(a), $\therefore$ ~P(a) is: Logic puzzles me, $\therefore$ logic is unintelligible.
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