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. || || || ||
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. || || || ||
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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Question
Give formal well-written proofs when you are proving a result or a counter example otherwise.
(Accidentally submitted a question without important 2nd half of question)
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.
Expert Solution
Step 1: State the problem
We will 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 .
Since 3k - 3 is an integer, 3n - 8 is odd.
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