Let P(n) be the statement that n-cent postage can be formed using just 4-cent an

Question

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 18, using the steps below. First, we prove P(n) by regular induction. Prove (i) P(18), and (ii) P(k) rightarrow P(k + 1) for all k 18. Now, we prove P(n) by strong induction. Prove that P(18), P(19), P(20) and P(21) to complete the basis step. For the inductive step, state clearly what you can assume and what you need to prove. Now. prove the inductive step and explain why this complete vour proof.

Explanation / Answer

http://web.mnstate.edu/jamesju/Fall2011/Content/M310HW7Solns.pdf

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