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 E 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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Please find all three falses
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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