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: 43

Answer

Let\[p\]be: Person is a chemist. Let\[q\]be: Person has a college degree. The form of the premises is \[\begin{align} & \underline{\begin{align} & p\to q \\ & \sim q \\ \end{align}}\ \ \ \ \ \underline{\begin{array}{*{35}{l}} \text{If a person is a chemist, then that person has a college degree}\text{.} \\ \text{My best friend does not have a college degree}\text{.} \\ \end{array}} \\ & \therefore \ \ \ \ ?\ \ \ \ \ \ \ \ \ \text{Therefore, } \\ \end{align}\] The conclusion \[\sim p\] is valid because it forms the contrapositive reasoning of a valid argument when it follows the given premises. The conclusion \[\sim p\] translates as my best friend is not a chemist. Therefore, the valid conclusion from the provided premises is, my best friend is not a chemist. The valid conclusion from the provided premises is, my best friend is not a chemist.
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