Explain why or why not the proof of the following result is correct or not correct. Let n be and integer. If 3n - 8 is odd, then n is odd. Proof. Assume that n is odd. Then n = 2k + 1 for some integer k. Then 3n - 8 3(2k + 1)-8 6k+3-8 6k-5 2(3k - 3) + 1. || || || ||

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 25E
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Give formal well-written proofs when you are proving a result or a counter example otherwise. 

 

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III.
Explain why or why not the proof of the following result is correct or not correct.
Let n be and integer. If 3n – 8 is odd, then n is odd.
Proof. Assume that n is odd.
3n - 8
=
=
=
Then n = 2k + 1 for some integer k. Then
3(2k + 1) - 8
6k+ 3-8
6k-5
=
2(3k-3) + 1.
Since 3k - 3 is an integer, 3n – 8 is odd. Q.E.D.
Transcribed Image Text:III. Explain why or why not the proof of the following result is correct or not correct. Let n be and integer. If 3n – 8 is odd, then n is odd. Proof. Assume that n is odd. 3n - 8 = = = Then n = 2k + 1 for some integer k. Then 3(2k + 1) - 8 6k+ 3-8 6k-5 = 2(3k-3) + 1. Since 3k - 3 is an integer, 3n – 8 is odd. Q.E.D.
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