Discrete Mathematics with Applications 4th Edition

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

Chapter 2 - The Logic of Compound Statements - Exercise Set 2.1 - Page 38: 45


The two statements in a and b are logically equivalent

Work Step by Step

Assign each quality to a variable, Double math major = x, Math major = y, Computer Science major = z Look at what both statements claim is true A states that for Bob x∧z holds true, and that for Ann, y∧(~(x∧z)) holds true B states that for one of Bob and Ann ~(x∧z) holds true. B also states that for Ann, y holds true, and for Bob, x∧z holds true. Using this new information we can assume that the ~(x∧z) case described earlier applies to Ann, as it contradicts the case for Bob, therefore y∧(~(x∧z)) holds true for Ann. The two final logic statements for each person from each statement match, with Bob being x∧z, and Ann being y∧(~(x∧z)), therefore the two statements are logically equivalent.
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.