Problem 10: 1. Determine which amount of postage can be formed using just 4 - cent and 11 - cent stamps. 2. Prove your answer to (i) using mathematical induction.
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We can use three 4 cent stamps and one 11 cent stamp to form 23 cents. So, the smallest amount is 23 cents. Now, let's try to prove that any amount greater than or equal to 23 cents can be formed using just 4 cent and 11 cent stamps. Base Case: We have already Show more…
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a) Determine which amounts of postage can be formed using just 4 -cent and 11 -cent stamps. b) Prove your answer to (a) using the principle of math- ematical 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 that in the inductive hypothesis for a proof using mathematical induction?
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Strong Induction and Well-Ordering
Supreeta N.
2. a) Which amounts of postage can be formed using only 4-cent and 9-cent stamps? b) Prove the conjecture you made using regular induction. c) Prove the conjecture you made using strong induction.
Sri K.
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