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 192: 45

Answer

Let\[p\]be the writers of My Mother the Car improve their scripts. Let\[q\]be the writers of My Mother the Car dropped from prime time. The form of the premises is \[\begin{align} & \underline{\begin{align} & p\vee q \\ & \\ & \tilde{\ }p \\ \end{align}}\ \ \ \ \ \underline{\begin{array}{*{35}{l}} \begin{array}{*{35}{l}} \text{The writers of My Mother the Car were told by the network to improve their scripts} \\ \text{or be dropped form prime time}\text{.} \\ \end{array} \\ \text{The writers of My Mother the Car did not improve their scripts}\text{.} \\ \end{array}} \\ & \therefore \ \ ?\ \ \ \ \ \ \ \ \ \ \ \text{Therefore, } \\ \end{align}\] The conclusion \[q\] is valid because it forms the disjunctive reasoning of a valid argument when it follows the given premises. The conclusion can be translated as they were dropped from prime time. Therefore, the valid conclusion from the provided premises is the writers of My Mother were dropped from prime time.
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