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.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 42E
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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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