Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.6 Negations of Conditional Statements and De Morgan's Law - Exercise Set 3.6 - Page 179: 63

Answer

An example of disjunction is “Your workouts are strenuous or you do not get stronger.” The negation of disjunction statement is “your workouts are not strenuous and you get stronger.”

Work Step by Step

To understand the problem, we will take the following example: Example: Consider an example of disjunction “Your workouts are strenuous or you do not get stronger.” The negation of disjunction statement is “your workouts are not strenuous and you get stronger.” From provided statement, “The disjunction that is true, even though one of its component statements is false.” Consider pYour workouts are strenuous, as true part and qyou do not get stronger, as false part. The symbolic form of disjunction is\[p\vee q\]. By using the truth value of p and q in symbolic representation, \[T\vee F\equiv T\] The negation of truth value of \[T\vee F\] is F. Hence, the negation is false.
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