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 n2 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 n2 18? (c) What do you need to prove in the inductive step of a proof that P(n) is true for all integers n 2 18? (d) Complete the inductive step for k 21. (e) Explain why these steps show that P(n) is true for all integers n 2 18.

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 n2 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 n2 18? (c) What do you need to prove in the inductive step of a proof that P(n) is true for all integers n 2 18? (d) Complete the inductive step for k 21. (e) Explain why these steps show that P(n) is true for all integers n 2 18.

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Description: 9.Let P(n) be the statement that a postage of n cents can be formed using just 4-centstamps and 7-cent stamps. The parts of this exercise outline a strong induction proofthat P(n) is true for all integers n 2 18.(a) Show that the statements P(18), P

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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9.
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 2 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 n2 18?
(c) What do you need to prove in the inductive step of a proof that P(n) is true for
all integers n 2 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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