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 194: 78

Answer

The original argument in words for the contrapositive reasoning is if the grass is not wet then it is not raining.

Work Step by Step

Let p and q represent two simple statements. p : if it is raining. q : the grass is wet. Therefore, It is a conditional statement the grass is wet dependent on a condition when it is raining. Contrapositive reasoning form is interchanged between the hypothesis and a conclusion of a conditional statement and negating both. Its contrapositive reasoning form is: \[\begin{align} & \underline{\begin{align} & p\to q \\ & \text{ }\sim p \\ \end{align}} \\ & \therefore \sim q \\ \end{align}\] Hence, the original argument in words for the contrapositive reasoning is if the grass is not wet then it is not raining.
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