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

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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
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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.
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