5.2.6        Discrete MathematicsA) determine which amounts of postage can be formed using just 3 - cent and 10 - cent  stamps.                  3,6,9,10,12,13,15,16,18,19,21,23,24,26,27,29,30,...,L*3+H*10B) prove your answer to (A) using the principal of mathematical induction. Be sure to state explicitly your inductive hypothesis and the inductive steps.

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Asked Jun 2, 2019
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5.2.6        Discrete Mathematics

  1. A) determine which amounts of postage can be formed using just 3 - cent and 10 - cent  stamps.

                  3,6,9,10,12,13,15,16,18,19,21,23,24,26,27,29,30,...,L*3+H*10

  1. B) prove your answer to (A) using the principal of mathematical induction. Be sure to state explicitly your inductive hypothesis and the inductive steps.

   

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Expert Answer

Step 1

B)

Known fact:

Base step: Show it is true for first case, usually n =1.

Induction step: Show that if n = k is true then n = k+1 is also true.

Step 2

Base step:

Let us show the induction is true for P(19).

P(19) = one 10 cent stamp + three 3 cent stamps.

Induction step:

Let us assume that the induction is true for n.

That is, n postage amount can be formed using 10 cents and 3 cents stamps.

Now it is necessary to show that the induction is true for n + 1.

Step 3

Case 1:

If there are no 10 cents in n, then remove three cents stamps and add one 10 cent stamps to get n +1.

If n=18,

P(18) = six 3 cents stamp

There is no 10 cents stamps thus, remove three 3 cents stamp and add one 10 cents.

That is, P(18) = six 3 cents stamp – three 3 cent stamp + one 10 cents stamp.

     &nbs...

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