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

Answer

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.
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