Question

5. [9 Pts] Let $P(n)$ be the statement that $n$-cent postage can be formed using just 4-cent and 7-cent stamps. Prove that $P(n)$ is true for all $n ge 18$, using the steps below. (a) First, prove $P(n)$ by regular induction. State your basis step and inductive step clearly and prove them. (b) Now, prove $P(n)$ by strong induction. Again, state and prove your basis step and inductive step. Your basis step should have multiple cases.

          5. [9 Pts] Let $P(n)$ be the statement that $n$-cent postage can be formed using just 4-cent and
7-cent stamps. Prove that $P(n)$ is true for all $n ge 18$, using the steps below.
(a) First, prove $P(n)$ by regular induction. State your basis step and inductive step clearly
and prove them.
(b) Now, prove $P(n)$ by strong induction. Again, state and prove your basis step and
inductive step. Your basis step should have multiple cases.

5. [9 Pts] Let P(n) be the statement that n-cent postage can be formed using just 4-cent and
7-cent stamps. Prove that P(n) is true for all n ge 18, using the steps below.
(a) First, prove P(n) by regular induction. State your basis step and inductive step clearly
and prove them.
(b) Now, prove P(n) by strong induction. Again, state and prove your basis step and
inductive step. Your basis step should have multiple cases.

Added by Christopher V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

02/22/2023

Step 1

P(18): 18 = 4(4) + 7(1) P(19): 19 = 4(3) + 7(1) P(20): 20 = 4(5) P(21): 21 = 7(3) So, the basis step holds. Inductive Step: Assume P(n) is true for some n ≥ 18. We need to show that P(n+1) is also true. Since P(n) is true, we can write n = 4a + 7b for some Show more…

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