2008.semester.2

2008.semester.2 - CS202 DISCRETE MATHEMATICS SEMESTER...

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* This is a closed book, closed notes examination. * SHOW ALL WORK * The numbers in parentheses after each question is the number of points allocated to that question. * Write your answers on the examination paper in legible ink or pencil. If your answer cannot be read or understood, or if your answer is vague or confused, it will be marked wrong. * NAME ( Print Legibly. All Capitals ): PLEDGE ( Write Out In Full And Sign ): CS202 - D ISCRETE M ATHEMATICS S EMESTER E XAMINATION 2 F ALL 2008 Time Limit - Seventy Five Minutes

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Page 1 Department of Computer Science CS 202 University of Virginia Page score 1. Prove by induction that n 3 - n is divisible by three for any n 1. (10) 2. Prove using a direct proof that the difference between an even integer and an odd integer is odd. (10) 3. Prove using a proof by contradiction that for any integer n , if 3 n + 2 is odd, then n is odd. (10 pts)
Page 2 Department of Computer Science CS 202 University of Virginia Page score 4. Suppose each computer purchased by a company is equally likely to be a Dell or a Lenovo. If the company buys four computers, what is the probability that: (a) All four computers are from the same manufacturer. (5)

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