1. For each of the following statements: if the statement is true, then give a proof; if the statement is false, then write out the negation and prove that. (a) There exists an integer n, so that n³ - n is odd. (b) √6 is irrational. (c) For all a, b = Z, if a > 1 and b > 1, then gcd (2a, 2b) = 2 gcd(a, b).

1. For each of the following statements: if the statement is true, then give a proof; if the statement is false, then write out the negation and prove that. (a) There exists an integer n, so that n³ - n is odd. (b) √6 is irrational. (c) For all a, b = Z, if a > 1 and b > 1, then gcd (2a, 2b) = 2 gcd(a, b).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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