5.2.6          Discrete Mathematics (I filled in as much as I could) A) determine which amounts of postage can be formed using just 3 - cent and 10 - cent  stamps. 3,6,9,10,12,13,15,16,18,19,21,23,24,26,27,29,30,...,L*3+H*10 C) prove your answer to (a) using strong induction. How does this inductive hypothesis in this proof differ from that in the inductive hypothesis for proof using mathematical induction? Base step: need to show is T for 3,13,26 Statment of the Base Step: 3 = L*3+H*10 non-negative integers 13 = L*3+H*10 non-negative integers 26 = L*3+H*10 non-negative integers Statment of the Base Step: 3 = 1*3+0*10 13 = 1*3+1*10 26 = 2*3+2*10 Statement of the inductive step       Proof of the inductive step       Invoke the principle of strong induction Since the base step and the inductive step are true by the principle of strong induction all amounts of postage __________ can be obtained using 3 and 10 cent stamps

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 22E: Let x and y be integers, and let m and n be positive integers. Use mathematical induction to prove...
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5.2.6          Discrete Mathematics

(I filled in as much as I could)

  1. A) determine which amounts of postage can be formed using just 3 - cent and 10 - cent  stamps.

3,6,9,10,12,13,15,16,18,19,21,23,24,26,27,29,30,...,L*3+H*10

  1. C) prove your answer to (a) using strong induction. How does this inductive hypothesis in this proof differ from that in the inductive hypothesis for proof using mathematical induction?

Base step:

need to show is T for 3,13,26

Statment of the Base Step:

3 = L*3+H*10 non-negative integers

13 = L*3+H*10 non-negative integers

26 = L*3+H*10 non-negative integers

Statment of the Base Step:

3 = 1*3+0*10

13 = 1*3+1*10

26 = 2*3+2*10

Statement of the inductive step

 

 

 

Proof of the inductive step

 

 

 

Invoke the principle of strong induction

Since the base step and the inductive step are true by the principle of strong induction all amounts of postage __________ can be obtained using 3 and 10 cent stamps

 

 

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