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Claim: For every odd integer n, n² - 1 is a multiple of 8. Purported proof: Suppose there is an integer m where n² - 1 = 8m. Thus, n² = 8m + 1. Since 8m must be even, 8m+1 must be odd. Hence n² is odd, and so n must be an odd integer. (a) In your opinion, which of the following statements best describes the claim and purported proof above? Briefly explain your choice. 1. The claim itself is false, and thus the proof must be invalid. 2. The claim is true, but the proof has an error. 3. The claim is true, and the proof is logically valid. But it is not written well (e.g., hard to follow, lack of explanations between steps, etc.). 4. The claim is true, and the proof is correct and well-presented. (Hint: It's not this case.) (b) If you decided in (a) that the given claim and purported proof belongs to Case 1,2, or 3, provide a revision of the claim and/or the proof that would belong to Case 4.

Claim: For every odd integer n, n² - 1 is a multiple of 8. Purported proof: Suppose there is an integer m where n² - 1 = 8m. Thus, n² = 8m + 1. Since 8m must be even, 8m+1 must be odd. Hence n² is odd, and so n must be an odd integer. (a) In your opinion, which of the following statements best describes the claim and purported proof above? Briefly explain your choice. 1. The claim itself is false, and thus the proof must be invalid. 2. The claim is true, but the proof has an error. 3. The claim is true, and the proof is logically valid. But it is not written well (e.g., hard to follow, lack of explanations between steps, etc.). 4. The claim is true, and the proof is correct and well-presented. (Hint: It's not this case.) (b) If you decided in (a) that the given claim and purported proof belongs to Case 1,2, or 3, provide a revision of the claim and/or the proof that would belong to Case 4.

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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Claim: For every odd integer n, n² – 1 is a multiple of 8. Purported proof: Suppose there is an integer m where n² - 1 = 8m. Thus, n² = 8m + 1. Since 8m must be even, 8m+1 must be odd. Hence n² is odd, and so n must be an odd integer. (a) In your opinion, which of the following statements best describes the claim and purported proof above? Briefly explain your choice. 1. The claim itself is false, and thus the proof must be invalid. 2. The claim is true, but the proof has an error. 3. The claim is true, and the proof is logically valid. But it is not written well (e.g., hard to follow, lack of explanations between steps, etc.). 4. The claim is true, and the proof is correct and well-presented. (Hint: It's not this case.) (b) If you decided in (a) that the given claim and purported proof belongs to Case 1,2, or 3, provide a revision of the claim and/or the proof that would belong to Case 4.
Transcribed Image Text:Claim: For every odd integer n, n² – 1 is a multiple of 8. Purported proof: Suppose there is an integer m where n² - 1 = 8m. Thus, n² = 8m + 1. Since 8m must be even, 8m+1 must be odd. Hence n² is odd, and so n must be an odd integer. (a) In your opinion, which of the following statements best describes the claim and purported proof above? Briefly explain your choice. 1. The claim itself is false, and thus the proof must be invalid. 2. The claim is true, but the proof has an error. 3. The claim is true, and the proof is logically valid. But it is not written well (e.g., hard to follow, lack of explanations between steps, etc.). 4. The claim is true, and the proof is correct and well-presented. (Hint: It's not this case.) (b) If you decided in (a) that the given claim and purported proof belongs to Case 1,2, or 3, provide a revision of the claim and/or the proof that would belong to Case 4.
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