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: 4

Answer

a. Jennifer and Teja are not friends. b. There are fewer or greater than 13 items in a baker’s dozen. c. Abby sent 100 or fewer text messages at least one day. d. 121 is not a perfect square.

Work Step by Step

The negation of a proposition can be obtained by prefixing the proposition with "It is not the case that". As a further, optional step, the resulting sentence can be reconstructed to a more natural form to make it simpler or it's effective meaning clearer. a. “It is not the case that Jennifer and Teja are friends” or the less verbose “Jennifer and Teja are not friends.” b. “It is not the case that there are 13 items in a baker’s dozen” or “There are fewer or greater than 13 items in a baker’s dozen.” c. “It is not the case that Abby sent more than 100 text messages every day” or “Abby sent 100 or fewer text messages at least one day.” d. “It is not the case that 121 is a perfect square” or “121 is not a perfect square.”
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