hw2-solutions - CS 173 Discrete Structures Fall 2010...

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CS 173: Discrete Structures, Fall 2010 Homework 2 Solutions This homework contains 5 problems worth a total of 47 points. 1. [9 points] Translating notation into English Suppose we define: F ( x ) is “x plays Fate.” B ( x ) is “x plays banjo.” K ( x ) is “x likes kimchi.” L ( x,y ) is “x likes y.” P ( x ) is “x has taken CS 125.” S is the set of all students. Translate the following into English: • ∀ x S, P ( x ) ( F ( x ) K ( x )) • ∀ x S, K ( x ) ( ¬ B ( x ) F ( x )) • ∃ x,y S, ( P ( y ) B ( x )) L ( x,y ) Solutions (a) Every student who has taken CS 125 either plays fate or likes kimchi. (b) Every student likes kimchi and, if he/she doesn’t play banjo, he/she plays Fate. (c) There is a pair of students x and y where y has taken CS 125 or x plays banjo, and also x likes y . 2. [12 points] Negating statements Negate the following logic statements. Be sure to move all instances of ¬ onto indi- vidual propositions or predicates.
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