Unformatted text preview: Proof: Let P ( n ) be the predicate “n = n + 1”. To show that P ( k ) → P ( k + 1), assume that P ( k ) is true for some k , so that k = k + 1. Add 1 to both sides of this equation to obtain k + 1 = k + 2, which is P ( k + 1). Therefore P ( k ) → P ( k + 1) is true. Hence P ( n ) is true for all positive integers n . Problem 2.5, 6 points. Sharing a chocolate bar. Problem 10 from Section 4.2 of Rosen’s textbook. Problem 2.6, 6 points. Describe a recursive algorithm for computing 5 2 n where n is a nonnegative integer. Problem 2.7, 6 points. Problem 38 from Section 4.4 of Rosen’s textbook....
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 Spring '05
 HUANG
 Mathematical Induction, Natural number

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