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Assignment #1 + Solution Winter 2009

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Computer Science
CS 245
Nancy Day

CS 245 Winter 2009 Assignment 1 Due: Thu 22 Jan 2009 10am in the CS245 Drop Boxes 27 marks SOLUTION SET There are multiple correct answers to some of these questions. 1. (9 marks) Express each of the following sentences as a formula in propositional logic. For each proposition letter you use, be sure to state the English phrase it represents. (a) The class was held although the weather was warm. h ∧ w where • h – the class was held • w – the weather was warm (b) It rains when it is not winter. ¬w ⇒ r where • r – it rains • w – it is winter 1 (c) I will go grocery shopping exactly if it is not snowing and I have money. g ⇔ ¬s ∧ m where • g – I will go grocery shopping • s – it is snowing • m – I have money 2. (6 marks) For the following¬(b ⇒ a),b ∨ c ⊢ c (a) (4 marks) Do the premises logically imply the conclusion? Explain your response and demonstrate that your response is correct using the semantics of propositional logic. No, the premises do not logically imply the conclusion. The following Boolean valuation, v, is a counterexample where the premises are T and the conclusion is F. v(a) = F,v(b) = T,v(c) = F Demonstration: Premise 1: v(¬(b ⇒ a)) = NOT (v(b) IMP v(a))
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