2. Suppose that instead of proving the claim "there is no integer n such that n= 2 mod 6 and n7 mod 9," we instead wanted to prove the similar claim that "there is no integer n such that n2 mod 6 and n8 mod 9." Make the appropriate adjustments to the tutorial proof and determine whether the adjusted proof by contradiction can prove the claim to be true. a. The adjusted proof works, and thus the new claim is true. b. The adjusted proof does not work, but the new claim is still true. e. The adjusted proof does not work, and the new claim is now false.

2. Suppose that instead of proving the claim "there is no integer n such that n= 2 mod 6 and n7 mod 9," we instead wanted to prove the similar claim that "there is no integer n such that n2 mod 6 and n8 mod 9." Make the appropriate adjustments to the tutorial proof and determine whether the adjusted proof by contradiction can prove the claim to be true. a. The adjusted proof works, and thus the new claim is true. b. The adjusted proof does not work, but the new claim is still true. e. The adjusted proof does not work, and the new claim is now false.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...

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