In each of the following statements, n represents a positive integer. One of the statements is true, the other is false. (I) For all n, the integer 9n + 7 is a multiple of 8. (II) For all n, the integer 9n + 6 is a multiple of 5. (a) Write down which statement is false and give a counter-example to show that it is false. (b) Prove the other statement by mathematical induction.

In each of the following statements, n represents a positive integer. One of the statements is true, the other is false. (I) For all n, the integer 9n + 7 is a multiple of 8. (II) For all n, the integer 9n + 6 is a multiple of 5. (a) Write down which statement is false and give a counter-example to show that it is false. (b) Prove the other statement by mathematical induction.

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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In each of the following statements, n represents a positive integer. One of the statements is true, the other is false.

(I) For all n, the integer 9n + 7 is a multiple of 8.

(II) For all n, the integer 9n + 6 is a multiple of 5.

(a) Write down which statement is false and give a counter-example to show that it is false.

(b) Prove the other statement by mathematical induction.

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