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(a) If n is a real number such that n>1 , then n>1. Suppose that n'>1. Then n>1 . (b) The number log, 3 is irrational if it is not the ratio of two integers. Therefore, since log,3 cannot be written in the form where a and b are integers, it is irrational. (c) If n is a real number and n>3, then n²>9. Suppose that n's 9. Then ns 3. n°s

(a) If n is a real number such that n>1 , then n>1. Suppose that n'>1. Then n>1 . (b) The number log, 3 is irrational if it is not the ratio of two integers. Therefore, since log,3 cannot be written in the form where a and b are integers, it is irrational. (c) If n is a real number and n>3, then n²>9. Suppose that n's 9. Then ns 3. n°s

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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ount t (e) If n is a real number and n>2 , then n'>4. If ns 2, then Determine whether the following arguments are valid or not. If an argument is valid, which rule of inference is used? If not which fallacy occurs? (a) If n is a real number such that n>1, then n'>1. Suppose n'>1 . Then n>1 . (b) The number log, 3 is irrational if it is not the ratio of two integers. Therefore, since log23 cannot be written in the a where a and b are integers, it is irrational. b. form (c) If n is a real number and n>3, then n'>9. Suppose that n°s (d) Either a positive integer is a perfect square or it has an even number of positive integer divisors. If n is a positive integer 69. Then ns 3. dotao that has an odd number of positive integer divisors, then t o a perfect square. n's 4. then 2 10. 2.
Transcribed Image Text:ount t (e) If n is a real number and n>2 , then n'>4. If ns 2, then Determine whether the following arguments are valid or not. If an argument is valid, which rule of inference is used? If not which fallacy occurs? (a) If n is a real number such that n>1, then n'>1. Suppose n'>1 . Then n>1 . (b) The number log, 3 is irrational if it is not the ratio of two integers. Therefore, since log23 cannot be written in the a where a and b are integers, it is irrational. b. form (c) If n is a real number and n>3, then n'>9. Suppose that n°s (d) Either a positive integer is a perfect square or it has an even number of positive integer divisors. If n is a positive integer 69. Then ns 3. dotao that has an odd number of positive integer divisors, then t o a perfect square. n's 4. then 2 10. 2.
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