Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.3 Truth Tables for Negation, Conjunction and Disjunction - Exercise Set 3.3 - Page 148: 70

Answer

The given statement in symbolic form is\[\sim \left( p\vee q \right)\wedge \left( \sim p\wedge \sim q \right)\].

Work Step by Step

\[p\]: \[x<5\], and \[q\]: \[x>8\]. The given statement first shows the negation of the disjunction of the statement\[p\]and the statement \[q\]and then the conjunction of\[\left( \sim p\wedge \sim q \right)\]. Hence, the given statement in symbolic form is\[\sim \left( p\vee q \right)\wedge \left( \sim p\wedge \sim q \right)\]. The truth table for the given statement is below:
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