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Of the statements below, three are false and one is true. Find two of the false statements and give counterexamples to them. (You don't have to do the calculations for a counterexample if you can explain why it's going to work. find all three false statements. I. For all n € N, if you multiply n by 3 and add the digit 7 to the end (e.g. 5 becomes 15, which becomes 157), the final result will be prime. II. For all n € N, 3" + 2 is never divisible by 7. III. If a, b, c are real numbers such that a+b, a+c, and b+c are all rational, then a+b+c is rational. IV. For all n € N, n. 2">n!.

Of the statements below, three are false and one is true. Find two of the false statements and give counterexamples to them. (You don't have to do the calculations for a counterexample if you can explain why it's going to work. find all three false statements. I. For all n € N, if you multiply n by 3 and add the digit 7 to the end (e.g. 5 becomes 15, which becomes 157), the final result will be prime. II. For all n € N, 3" + 2 is never divisible by 7. III. If a, b, c are real numbers such that a+b, a+c, and b+c are all rational, then a+b+c is rational. IV. For all n € N, n. 2">n!.

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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Of the statements below, three are false and one is true. Find two of the false statements and give counterexamples to them. (You don't have to do the calculations for a counterexample if you can explain why it's going to work. find all three false statements. I. For all n € N, if you multiply n by 3 and add the digit 7 to the end (e.g. 5 becomes 15, which becomes 157), the final result will be prime. II. For all n € N, 3" +2 is never divisible by 7. III. If a, b, c are real numbers such that a+b, a+c, and b+c are all rational, then a+b+c is rational. IV. For all n EN, n.2" >n!.
Transcribed Image Text:Of the statements below, three are false and one is true. Find two of the false statements and give counterexamples to them. (You don't have to do the calculations for a counterexample if you can explain why it's going to work. find all three false statements. I. For all n € N, if you multiply n by 3 and add the digit 7 to the end (e.g. 5 becomes 15, which becomes 157), the final result will be prime. II. For all n € N, 3" +2 is never divisible by 7. III. If a, b, c are real numbers such that a+b, a+c, and b+c are all rational, then a+b+c is rational. IV. For all n EN, n.2" >n!.
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