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: 44

Answer

Let\[p\]be the Westway Expressway is not in operation. Let\[q\]be automobile traffic makes the East Side Highway look like a parking lot. The form of the premises is \[\begin{align} & \underline{\begin{align} & p\to q \\ & \\ & p \\ \end{align}}\ \ \ \ \ \underline{\begin{align} & \text{If the Westway Expressway is not in operation, } \\ & \text{automobile traffic makes the East Side Highway look like a parking lot}\text{.} \\ & \text{On June 2, the Westway Expressway was completely shut down because of an overturned truck}\text{.} \\ \end{align}} \\ & \therefore ?\ \ \ \ \ \ \ \ \ \ \ \ \ \text{Therefore, } \\ \end{align}\] The conclusion \[q\] is valid because it forms the direct reasoning of a valid argument when it follows the given premises. The conclusion can be translated as automobile traffic makes the East Side Highway look like a parking lot. Therefore, the valid conclusion from the provided premises is automobile traffic makes the East Side Highway look like a parking lot.
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