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 1.1 - Propositional Logic - Exercises - Page 15: 24

Answer

a) If you send me an email message, I will remember to send you the address. If you do not send me an email message, I will not remember. b) If you were born in the United States, you are a citizen of this country. c) If you keep your textbook, it will be a useful reference in your future courses. d) If their goalie plays well, the Red Wings will win the Stanley Cup. e) If you get the job, you had the best credentials. f) If there is a storm, the beach erodes. g) If you have a valid password, you can log on to the server. If you do not have a valid password, you cannot log on to the server. h) If you begin your climb too late, you will not reach the summit. If you begin before it gets too late, you will reach the summit.

Work Step by Step

To solve this problem, substitute one phrase as $p$ and the other $q$. Create the basic "if $p$, then $q$" structure using this representation and then replace the phrases to create the sentence in English. The replacements are: a) p;q - I will remember to send you the address q;p - you send me an email message b) q - be a citizen of this country p - be born in the United States c) p - you keep your textbook q - it is a useful reference in your future courses d) q - the Red Wings win the Stanley Cup p - their goalie plays well e) p - you get the job q - you had the best credentials f) q - the beach erodes p - there is a storm g) p;q - have a valid password q;p - log on to the server h) q - you reach the summit p - you begin your climb too late
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