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2006.final

# 2006.final - CS202 DISCRETE MATHEMATICS FINAL EXAMINATION...

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* This is a closed book, closed notes examination. * 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. * The numbers in parentheses after each question is the number of points allocated to that question. NAME ( Print Legibly. All Capitals ): PLEDGE ( Write Out In Full And Sign ): Check that this copy of the examination has pages numbered 1 through 8. READ THE QUESTION BEFORE YOU ANSWER IT CS202 - D ISCRETE M ATHEMATICS F INAL E XAMINATION F ALL 2006 Time Limit - Three Hours

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Page 1 Department of Computer Science CS 202 University of Virginia Page score 1. Write a formal version of the following English texts: (Be careful to provide any declarations and definitions that are needed.) (a) If a student in CS202 gets more than 90% on the final, he or she will get an A in the course . (4) (b) Students in CS202 studied propositions, predicates, set theory, and functions . (4) (c) Less than 10 students in CS202 have taken a course in Physics . (4) (d) All of the students in CS202 have studied proof techniques . (4) (e) The birthday of at least one student in CS202 is in December . (4)
Page 2 Department of Computer Science CS 202 University of Virginia Page score 2. A magic square is an n x n square of different natural numbers in which all rows, all columns, and the diagonals sum to the same value. Using three variables: an n

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