Thinking Mathematically (6th Edition)

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

Chapter 3 - Logic - 3.7 Arguments and Truth Tables - Exercise Set 3.7 - Page 191: 42

Answer

In the provided statements, consider p as some journalists learn about the invasion, q as the newspapers will print the news, r as the invasion was a secret,\[\tilde{\ }p\]as no journalists learned about the invasion, and \[\tilde{\ }r\]as the invasion will not be a secret. Therefore, express the premises and conclusion symbolically. \[\begin{align} & \,p\to q \\ & \frac{\begin{align} & q\to \tilde{\ }r \\ & \sim p \\ \end{align}}{\therefore \,r} \\ \end{align}\] Here, sign \[\to \] denotes conditional means (if….then….), sign\[\sim \]denotes negation means it makes the sentence negative. The argument is basically transitive argument, i.e., it should be\[\sim r\], but the obtained conclusion is \[r\]. Therefore, it is a misuse of transitive argument. Hence, the argument is invalid
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