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Unformatted text preview: 8 Problem 8 A rational number is a real number that can be expressed as the ratio of two integers. An irrational number is a real number that is not rational. Provide an indirect proof of the following statement, i.e., prove the contrapositive. If a and b are real numbers and a · b is an irrational number, then either a or b is irrational. 9 Problem 9 Prove by induction that 1 1 · 3 + 1 3 · 5 + 1 5 · 7 + ··· + 1 (2 n1)(2 n + 1) = n 2 n + 1 . 10 Problem 10 Suppose that there are only two types of postage stamps, 4cent stamps and 5cent stamps. Prove that any amount of postage of 12 cents or greater can be made up out of 4cent and 5cent stamps. Hint: It is possible to prove this using strong induction over N . 11...
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This document was uploaded on 01/17/2012.
 Fall '09

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