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 2.3 - Page 62: 29

Answer

The argument is false due to inverse error

Work Step by Step

Let the two numbers be a and b. ∴ p is the statement that a|6 or b|6 (x|y translates to "x divides y") and q is the statement that (a$\times$b)|6 If at least one of these two numbers is divisible by 6, then the product of these two numbers is divisible by 6. (p → q) Neither of these two numbers is divisible by 6 (¬p) ∴ The product of these two numbers is not divisible by 6.(¬q) The argument follows the following logic: p → q ¬p ∴ ¬q Which, we know, is the inverse error
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