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 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 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?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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 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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