Unformatted text preview: 2 n > n. 4. Use induction to prove that every postage of 24 cents or more can be achieved using only 5-cent and 7-cent stamps. That is, prove that for every integer n ≥ 24, there exist some non-negative integers A and B such that P ( n ) : n = 7 A + 5 B. Let P ( n ) be the predicate “postage of n cents can be achieved.” Provide the inductive proof by using each of the following methods. (a) (Simple Induction) Prove the induction base, n = 24. Then, for any n ≥ 24, prove that if P ( n ) is true, then P ( n + 1) will be true. (b) (Strong Induction) Prove the induction base cases (24 , 25 , ··· , 30). Then for n ≥ 31, prove that: If P ( m ) is true for all 24 ≤ m < n , then P ( n ) is also true. 1...
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- Spring '09
- Negative and non-negative numbers, Dr. David Nassimi