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: 64

Answer

(a) The provided compound statement can be written in simple statements as\[p,q,r\]. Here, \[p,q,r\]represents two simple statements: \[p:\]I miss class. \[q:\] They take attendance \[r:\] There are pop quizzes. Therefore, the provided compound statement can be written in the symbolic form as: \[\sim p\leftrightarrow \left( q\vee r \right)\] (b) The truth table is as follows: c) So, from the truth table it can be stated that when the component of provided compound statement\[\sim p\leftrightarrow \left( q\vee r \right)\] has different truth value, then only resultant statement is false. Therefore, the statement is true when p is true and q and r are false.
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