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Let Zo(0,1,2,...). Order 7 of the following sentences so that they form a proof for the following statment Choose from these sentences: Then k=3(a+1)+7b, so the statement is also true when nk We use strong induction on n. Since 12k-3

Let Zo(0,1,2,...). Order 7 of the following sentences so that they form a proof for the following statment Choose from these sentences: Then k=3(a+1)+7b, so the statement is also true when nk We use strong induction on n. Since 12k-3

College Algebra (MindTap Course List)
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 43E
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Let Zo=(0,1,2,...} Order 7 of the following sentences so that they form a proof for the following statment Choose from these sentences: Then k=3(a+1)+7b, so the statement is also true when nk We use strong induction on n Since 12k-3<k, by the induction hypothesis we have k-3-3a+ 7b for some a,b € Z₂o Vnab((n ≥ 12)→ (n = 3a +76)), where the domain of discourse is Z₂0 x Z₂0 x Zo Now we will show that the statement is true for the case n k For the basis step, if n= 12, 13, 14, then the statement is true because 12-3-4+7-0. 13-3-2+7-1, and 14-3.0+7.2 By the induction hypothesis, we obtain that n is a multiple of 3 or 7 For the inductive step, let k 2 15 and assume that the statement is true for all integers n with 12 ≤n<k We use induction on a For the basis case, it a-0, we have n-3.0+7b7b By the strong induction the statement is true for all n212 Your Proof
Transcribed Image Text:Let Zo=(0,1,2,...} Order 7 of the following sentences so that they form a proof for the following statment Choose from these sentences: Then k=3(a+1)+7b, so the statement is also true when nk We use strong induction on n Since 12k-3<k, by the induction hypothesis we have k-3-3a+ 7b for some a,b € Z₂o Vnab((n ≥ 12)→ (n = 3a +76)), where the domain of discourse is Z₂0 x Z₂0 x Zo Now we will show that the statement is true for the case n k For the basis step, if n= 12, 13, 14, then the statement is true because 12-3-4+7-0. 13-3-2+7-1, and 14-3.0+7.2 By the induction hypothesis, we obtain that n is a multiple of 3 or 7 For the inductive step, let k 2 15 and assume that the statement is true for all integers n with 12 ≤n<k We use induction on a For the basis case, it a-0, we have n-3.0+7b7b By the strong induction the statement is true for all n212 Your Proof
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