a) Determine which amounts of postage can be formed using just 3-cent and 10-cent stamps.
b) Prove your answer to (a) using the principle of mathematical induction. Be sure to state explicitly your inductive hypothesis in the inductive step.
c) Prove your answer to (a) using strong induction. How does the inductive hypothesis in this proof differ from thatintheinductivehypothesisforaproofusingmathematical induction?

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Аноним Аноним · Answer 1 · 2019-10-16T00:23:57+02:00

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topeadeniran2 topeadeniran2 · Answer 2 · 2022-04-17T22:03:37+02:00

The postages that can be formed using just 3-cent and 10-cent stamps are linear combinations 3x + 10y.

Let P(n) = postage of n cents

n = 18

P(18) is true because 18 cents can be formed by using six 3 cent stamps.

By using the principle of mathematical induction, P(n) is true for all positive integers n.

Also, by using strong induction, P(n) will be postage of n cents that are formed by using 3 cent and 10 cent stamps.

n = 18, 19, and 20.

P(18) is true because 18 cents can be formed by using six 3-cent stamps.

P(19) is true because 19 cents can be formed by using one 10-cent stamp and there 3-cent stamps.

P(20) is true because 2 10-cent stamps can be used.

In conclusion, the principle of strong induction is true for all positive integers n.

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