Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.6 - Rules of Inference - Exercises - Page 78: 2

Answer

Argument form is modus tollens. Argument is valid Conclusion is true since premises are true.

Work Step by Step

Modua tollens: $$\displaylines{p \to q \cr \neg q \cr} $$$$- - - $$$$\therefore \neg p$$ Let us assume : p="George have eight legs" q="George is a spider". Then we can write the given argument as $$\displaylines{\neg p \to \neg q \cr q \cr} $$$$- - - $$$$\therefore p$$ $q\equiv \neg(\neg q)$ This can also be written as: $$\displaylines{\neg p \to \neg q \cr \neg(\neg q) \cr} $$$$- - - $$$$\therefore \neg(\neg p)$$ Then the conclusion is true according to modus tollens rule.
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