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)

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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