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 3.3 - Page 129: 11


a. There is a student who has seen Casablanca. b. All students have seen Star Wars. c. Every student has seen at least one movie. d. There is a movie that has been seen by every student. e. There are two different students who have seen the same movie. f. Every movie that a particular student has seen, has also been seen by another student.

Work Step by Step

Recall other ways to express the symbol $\forall$ include: for all, for every, for any, for each, for arbitrary, given any. Other ways to express the symbol $\exists$ include: there exists, there exist, there exists at least one, for some, for at least one, we can find a. When a statement contains more than one quantifier, we imagine the actions suggested by the quantifiers as being performed in the order in which the quantifiers occur.
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