Suppose you have only 3¢ and 5¢ stamps. (a) Find all values less than 10¢ for which you cannot form exact postage using only 3¢ and 5¢ stamps. (b) Let M be the integer that is one higher than the highest value from part (a). And let P be the predicate on N: P(n) "Exact postage for n¢ can be formed with only 3¢ and 5¢ stamps." Prove the following: Vn E N: (n 2 M)(P(n)).
Suppose you have only 3¢ and 5¢ stamps. (a) Find all values less than 10¢ for which you cannot form exact postage using only 3¢ and 5¢ stamps. (b) Let M be the integer that is one higher than the highest value from part (a). And let P be the predicate on N: P(n) "Exact postage for n¢ can be formed with only 3¢ and 5¢ stamps." Prove the following: Vn E N: (n 2 M)(P(n)).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose you have only 3¢ and 5¢ stamps.
(а)
Find all values less than 10¢ for which you cannot form exact postage using only 3¢ and 5¢
stamps.
(b)
Let M be the integer that is one higher than the highest value from part (a). And let P be the
predicate on N:
P(n)
"Exact postage for n¢ can be formed with only 3¢ and 5¢ stamps."
Prove the following:
Vn E N: (n > M)(P(n)).
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