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 190: 16


Use letters to represent each simple statement in the argument. p: Metro rail system is in operation. q: There are traffic delays. Express the premises and conclusion symbolically as: \[\frac{\begin{align} & \sim p\to q \\ & \sim q \\ \end{align}}{\therefore p}\ \ \ \ \ \ \frac{\begin{align} & \text{If a metro rail system is not in operation, there are traffic delays}\text{.} \\ & \text{Over the past year there have been no traffic delays}\text{.} \\ \end{align}}{\therefore \text{Over the past year a metro rail system has been in operation}\text{.}}\] The argument is in the form of Contra-positive Reasoning. Thus, the argument is valid.
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