Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.4 Truth Tables for the Conditional and the Biconditional - Exercise Set 3.4 - Page 160: 60

Answer

(a) The provided compound statement can be written in simple statements as\[p,q,r\]. Here, \[p,q,r\]represents three simple statements: \[p:\] You will take more than one class with lots of reading. \[q:\] You will have free time. \[r:\] You will be in the library until 1 a.m. Therefore, the provided compound statement can be written in the symbolic form as: \[p\to \left( \sim q\wedge r \right)\] (b) The truth table is as follows: c) So, from the truth table, it can be stated that when the truth value of \[p\to \left( \sim q\wedge r \right)\] is false,then the former statement is true and the latter statement is false. In rest, all other cases it is true. Therefore, the statement is true when p, q, and \[r\] are all false.
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