2007.final

# 2007.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 2007 Time Limit - Three Hours

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Page 1 Department of Computer Science CS 202 University of Virginia Page score 1. For each of the following, indicate which is a proposition, which a predicate, and which nei- ther. (Scoring: correct 0.5, incorrect -1 ) (a) CS202 fun ___________ (b) What is my grade in CS202? ___________ (c) UVA good_school CS fun_major ___________ (d) x + y + z > 5 ___________ (e) This month is December ___________ (f) ( b 2 - 4 ac ) / 2 a ___________ (g) Do not walk on the grass ___________ (h) George Bush is president ___________ (i) a > b c > d e > f ___________ (j) Please grade this examination quickly ___________ 2. For each of the following, carefully write the negation of the expression. (15) (a) c: computer | IBM ( c ) laptop ( c ) (b) c: computer | Apple ( c ) large_screen ( c ) (c) c: computer | Sun ( c ) ( d: computer | IBM ( d ) faster ( c, d )) 3. Draw a bipartite graph representation of the cartesian product A x B given A = {a, b, c} and B = {x, y} where the end points of each edge in the graph are a two-tuple from the product. (10)
Page 2 Department of Computer Science CS 202 University of Virginia Page score 4. Suppose that N is the set of nurses in a hospital and that R is the set of patient medical records on a hospital server. Suppose that the following propositions have been defined: (i) R_Nurse ( x, n )/ W_Nurse ( x, n ) is true if record x is readable/writable by nurse n ; (ii) R_Admin ( x )/ W_Admin

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2007.final - CS202 DISCRETE MATHEMATICS FINAL EXAMINATION...

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