Homework III Key

Homework III Key - Homework III Key Due: 22-Feb-2008...

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Homework III Key Due: 22-Feb-2008 Textbook: Mathematical Structures for Computer Science: A Modern Treatment of Discrete Structures   (5     th     Edition     ) J. Gersting, W.H. Freeman and Company: New York, NY . 2003. Problem #12, page 140  F(n) = F(n-2) + F(n-1)  = F(n-3) + F(n-4) + F(n-2) + F(n-3)  = 2F(n-3) + F(n-4) + F(n-2)  = 2[F(n-4) + F(n-5)] + F(n-4) + [F(n-3) + F(n-4)]  = 4F(n-4) + 2F(n-5) + F(n-3)  = 4F(n-4) + 2F(n-5) + [F(n-4) + F(n-5)]  = 5F(n-4) + 3F(n-5) QED  Problem #17, page 140  Base: F(2) = F(3) – 1 or 1 = 2 – 1 (true)  Assume: F(2) + . .. + F(2k) = F(2k + 1) – 1  WTS: F(2) + . .. + F(2(k+1)) = F(2(k+1) + 1) – 1  F(2) + . .. + F(2(k+1)) = F(2) + . .. + F(2k) + F(2(k+1))  = F(2k+1) – 1 + F(2(k+1))  = F(2k + 1) + F(2k + 2) – 1  = F(2k + 3) – 1  = F(2(k+1) + 1) – 1 QED  Problem #52, page 143 
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This homework help was uploaded on 04/19/2008 for the course CS 250 taught by Professor Michaelr.wick during the Spring '08 term at Wisc Eau Claire.

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Homework III Key - Homework III Key Due: 22-Feb-2008...

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