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 144: 32

Answer

The statements reordered and restated in if-then form (each statement is prefaced by $\forall x$ which is not rewritten to simplify): 2. If x is an example, then x is not arranged in regular order like the ones I'm used to. 4. If x is not arranged in regular order like the ones I'm used to, then I can't understand x. 1. In contrapositive form: If I can't understand x, then I grumble. 5. If I grumble at x, then x gives me a headache. 3. In contrapositive form: If x gives me a headache, then x is not easy. $\therefore$ these examples are not easy.

Work Step by Step

Universal transitivity: $\forall x, P(x) \rightarrow Q(x)$. $\forall x, Q(x) \rightarrow R(x)$. $\forall x, P(x) \rightarrow R(x)$.
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