# hw1 - CMPSC 360 Discrete Mathematics for Computer Science...

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CMPSC 360 Discrete Mathematics for Computer Science Fall 2009 Penn State University Assignment #1 Due: 31 August 1. Using propositional symbols R, S, T to stand for Rico, Sal, and Tony working, and O to stand for the shop being open, represent each of the following statements as propositional formulae: (a) Rico works whenever the shop is open. (b) At least two of them are working if the shop is open. (c) Tony and Sal work together. (d) If Rico only works when Tony works, then Sal works alone. 2. Use De Morgan’s laws to write negations of the following statements: (a) Either Sal or Tony is working. (b) Tony never works when the shop is open. (c) One of them is working. (d) Rico never works alone. 3. Let A, B, C stand for the propositions “Ann is a teacher,” “Ann is rich,” and “Ann is a movie star.” Now consider the three statements “Ann is a teacher,” “It is false that Ann is a teacher and Ann is rich,” and “If Ann is a movie star then Ann is rich.” Assume we wish to show that these three statements imply that it is false that Ann is a movie star. Give the required

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