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Question 2 Write a formal proof for each of the following claims; some of them were used in class. In what follows, K, a, b are positive integers. In each part you may use the previous parts of the question, even if you did not solve it. a) If b+ 0 and a | o then a sb. b) If a b and b| a then a b. e) Let K-b+c. If there exists a such that a | b and a K then a e. d) Let K=b+1. If there exists a> 1 such that a |b then a (K. Hint: Use proof by contradiction. That is, assume that both a | b and a K hold and then use Part a) to reach a contradiction.

Question 2 Write a formal proof for each of the following claims; some of them were used in class. In what follows, K, a, b are positive integers. In each part you may use the previous parts of the question, even if you did not solve it. a) If b+ 0 and a | o then a sb. b) If a b and b| a then a b. e) Let K-b+c. If there exists a such that a | b and a K then a e. d) Let K=b+1. If there exists a> 1 such that a |b then a (K. Hint: Use proof by contradiction. That is, assume that both a | b and a K hold and then use Part a) to reach a contradiction.

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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Question 2 Write a formal proof for each of the following claims; some of them were used in class. In what follows, K, a, b are positive integers. In each part you may use the previous parts of the question, even if you did not solve it. a) If b+ 0 and a | b then a < b. b) If a | b and b| a then a b. e) Let K - b+c. If there exists a such that a b and a | K then a e. d) Let K=6+1. If there exists a> 1 such that a b then a K. Hint: Use proof by contradiction. That is, assume that both a b and a | K hold and then use Part a) to reach a contradiction.
Transcribed Image Text:Question 2 Write a formal proof for each of the following claims; some of them were used in class. In what follows, K, a, b are positive integers. In each part you may use the previous parts of the question, even if you did not solve it. a) If b+ 0 and a | b then a < b. b) If a | b and b| a then a b. e) Let K - b+c. If there exists a such that a b and a | K then a e. d) Let K=6+1. If there exists a> 1 such that a b then a K. Hint: Use proof by contradiction. That is, assume that both a b and a | K hold and then use Part a) to reach a contradiction.
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