hw2ANSWERS - Neal Whittington (whittin3) CS 173: Discrete...

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Unformatted text preview: Neal Whittington (whittin3) CS 173: Discrete Structures, Spring 2010 Homework 2 This homework contains 6 problems worth a total of 50 points. It is due on Friday, February 5th at 4pm. 1. [9 points] Logic notation Translate the following sentences into propositional or predicate logic. (a) For every cookie that contains lots of butter, that cookie is tasty and also fatten- ing. ∀ x ∈ C,B ( x ) → ( T ( x ) ∧ F ( x )) C is the set of all cookies B(x) means x contains lots of butter T(x) means x is tasty F(x) means x is also fattening (b) Either the tablecloth is pink, or the tablecloth is white and the red light is shining on it. ( P ∨ W ) ∧ R P means the tablecloth is pink W means the tablecloth is white R means the red light is shining on it (c) There exists an integer, x, that is equal to its own negation. ∃ x Z ,x = ¬ x 2. [6 points] Translating notation into English Suppose we define: • C ( x ) is “x likes to cook.” • B ( x ) is “x plays banjo.” • T ( x ) is “x is on the CS 173 course staff.” • A ( x ) is “x is taking CS 232.” • S is the set of all students. 1 Translate the following into English: • ∃ x ∈ S,T ( x ) → ( C ( x ) ∨ A ( x )) Some Student that is on the CS173 course staff likes to cook or is taking CS232.Some Student that is on the CS173 course staff likes to cook or is taking CS232....
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This note was uploaded on 11/09/2011 for the course CS 173 taught by Professor Erickson during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw2ANSWERS - Neal Whittington (whittin3) CS 173: Discrete...

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