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4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts Page 363 of this exercise outline a strong induction proof that P(n) is true for all integers n ≥ 18. a) Show that the statements P(18), P(19), P(20), and P(21) are true, completing the basis step of a proof by strong induction that P(n) is true for all integers n ≥ 18. b) What is the inductive hypothesis of a proof by strong induction that P(n) is true for all integers n ≥ 18? c) What do you need to prove in the inductive step of a proof that P(n) is true for all integers n ≥ 18?

4. Let P(n) be the statement that a postage of n cents can be formed using just 4-cent stamps and 7-cent stamps. The parts Page 363 of this exercise outline a strong induction proof that P(n) is true for all integers n ≥ 18. a) Show that the statements P(18), P(19), P(20), and P(21) are true, completing the basis step of a proof by strong induction that P(n) is true for all integers n ≥ 18. b) What is the inductive hypothesis of a proof by strong induction that P(n) is true for all integers n ≥ 18? c) What do you need to prove in the inductive step of a proof that P(n) is true for all integers n ≥ 18?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 49E: 49. a. The binomial coefficients are defined in Exercise of Section. Use induction on to prove...
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4. Let P(n) be the statement that a postage of ʼn cents can be formed using just 4-cent stamps and 7-cent stamps. The parts Page 363 of this exercise outline a strong induction proof that P(n) is true for all integers n ≥ 18. a) Show that the statements P(18), P(19), P(20), and P(21) are true, completing the basis step of a proof by strong induction that P(n) is true for all integers n ≥ 18. b) What is the inductive hypothesis of a proof by strong induction that P(n) is true for all integers n ≥ 18? c) What do you need to prove in the inductive step of a proof that P(n) is true for all integers n ≥ 18? d) Complete the inductive step for k ≥ 21. e) Explain why these steps show that P(n) is true for all integers n ≥ 18.
Transcribed Image Text:4. Let P(n) be the statement that a postage of ʼn cents can be formed using just 4-cent stamps and 7-cent stamps. The parts Page 363 of this exercise outline a strong induction proof that P(n) is true for all integers n ≥ 18. a) Show that the statements P(18), P(19), P(20), and P(21) are true, completing the basis step of a proof by strong induction that P(n) is true for all integers n ≥ 18. b) What is the inductive hypothesis of a proof by strong induction that P(n) is true for all integers n ≥ 18? c) What do you need to prove in the inductive step of a proof that P(n) is true for all integers n ≥ 18? d) Complete the inductive step for k ≥ 21. e) Explain why these steps show that P(n) is true for all integers n ≥ 18.
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