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
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)
- 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
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