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 a
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Home » Mathematics » 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.