Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.2 - Page 117: 45

Answer

There exists a person who has a large income and is not happy.

Work Step by Step

Recall the definition of sufficient: "$\forall x$, r(x) is a sufficient condition for s(x)" means "$\forall x$, if r(x) then s(x)." In this case r(x) is: person has a large income. s(x) is: person is happy. Recall the form of the negation of a universal conditional statement: $~(\forall x, P(x) \rightarrow Q(x)) \equiv \exists x$ such that $(P(x) \land $ ~$Q(x))$ In this case, the negation is: $\exists$ x, such that r(x) and ~s(x), which is: "there exists a person who has a large income and is not happy."
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.