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 1.4 - Predicates and Quantifiers - Exercises - Page 53: 12


a) 0 b) 1 c) 0 d) 1 e) 0 f) 1 g) 0

Work Step by Step

Our domain is all integers. a) $Q(0)$ is the probability that $0+1>2(0)$, so $Q(0)=0$ b) $Q(−1)$ is the probability that $−1+1>2(−1)$, so $Q(−1)=1$ c) $Q(1)$ is the probability that $1+1>2(1)$, so $Q(1)=0$ d) $∃xQ(x)$ is satisfied by $x=−1$, so $∃xQ(x)=1$ e) $∀xQ(x)$ is contradicted by $Q(0)$, so $∀xQ(x)=0$ f) $∃x¬Q(x)$ is satisfied by $Q(1)$, so $∃x¬Q(x)=1$ g) $∀x¬Q(x)$ is contradicted by $Q(−1)$, so $∀x¬Q=0$
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