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 1.5 - Nested Quantifiers - Exercises - Page 64: 5

Answer

(a) Student Sarah Smith has visited the website www.att.com. (b) There is a student in your class that has visited the website www.imbd.org. (c) There is a website that José Orez has visited. (d) There is a website that Ashok Puri and Cidy Yoon have both visited. (e) There is a student in your class, beside David Belcher, that has visited all websites that David Belcher visited. (f) There are two different students in your class that have visited the same websites.

Work Step by Step

Given: W(x,y) =“ Student x has visited website y" Domain of x=All students in your class Domain of y=All websites INTERPRETATION SYMBOLS Conjunction $p \land q$: p and q Conditional statement $p \rightarrow q:$ if p, then q Biconditional statement $p \leftrightarrow q$: p if and only if q Existential quantification $\exists x P(x)$: There exists an element x in the domain such that P(x). Universal quantification $\forall xP(x)$: P(x) for all values of x in the domain. Answer (a) Student Sarah Smith has visited the website www.att.com. (b) There is a student in your class that has visited the website www.imbd.org. (c) There is a website that José Orez has visited. (d) There is a website that Ashok Puri and Cidy Yoon have both visited. (e) There is a student in your class, beside David Belcher, that has visited all websites that David Belcher visited. (f) There are two different students in your class that have visited the same websites.
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