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2007.semester.2

2007.semester.2 - CS202 DISCRETE MATHEMATICS SEMESTER...

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* This is a closed book, closed notes examination. * The numbers in parentheses after each question is the number of points allocated to that question. * Write your answers on the examination paper in ink or legible 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 2007 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: (10 pts) 2. A real number r is rational if there are integers p and q with q 0 such that r = p/q . Prove using a direct proof that if r and s are rational then r + s is rational. (10 pts) 3. Prove using a proof by contradiction that for any integer n , if 3 n + 2 is odd, then n is odd. (10 pts) r i i 0 = n r ( n 1 + 1 ) r 1 ( ) =
Page 2 Department of Computer Science CS 202 University of Virginia Page score 4. How many total

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