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Prove each of the following statements by using a direct proof, a proof by contrapositive, a proof by contradiction, or a proof by cases. Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. 1. For any integer n, if 3n – 5 is even, then n is odd. 2. For any real number x, ]x + 5| – x > 1.

Prove each of the following statements by using a direct proof, a proof by contrapositive, a proof by contradiction, or a proof by cases. Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. 1. For any integer n, if 3n – 5 is even, then n is odd. 2. For any real number x, ]x + 5| – x > 1.

Advanced Engineering Mathematics
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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Part V Prove each of the following statements by using a direct proof, a proof by contrapositive, a proof by contradiction, or a proof by cases. Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. 1. For any integer n, if 3n – 5 is even, then n is odd. 2. For any real number x, |x + 5| – x > 1.
Transcribed Image Text:Part V Prove each of the following statements by using a direct proof, a proof by contrapositive, a proof by contradiction, or a proof by cases. Indicate which proof method you used, as well as the assumption (i.e., what you suppose) and the conclusion (i.e., what you need to show) of the proof. 1. For any integer n, if 3n – 5 is even, then n is odd. 2. For any real number x, |x + 5| – x > 1.
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