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s09_a1

# s09_a1 - UNIVERSITY OF WATERLOO School of Computer Science...

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UNIVERSITY OF WATERLOO School of Computer Science CS245 Logic and Computation Spring 2009 ASSIGNMENT 1 (Due: Thursday, May 21, 2009 at 5:00pm) Use makeCover to produce a cover page for your assignment and hand in your assignment in the CS245 assignment box. Assignments are to be done individually. 1. (2 marks) Insert brackets into the following formulae so that we do not have to rely on the associativity and order of precedence of the logical connectives to understand the formulae. (a) p q ⇔ ¬ p ⇒ ¬ q p (b) a b c d e 2. (3 marks) Assuming standard rules of precedence and associativity, are the following well-formed for- mulae? If not, explain why not. (a) p q ¬ r (b) ¬ p ⇒ ¬ q (c) p ¬ ⇒ ¬ q 3. (6 marks) Express the following sentences as propositional formulas. Show the English phrase that your propositional symbols represent (e.g., p – “it is raining”). (a) When it rains it pours. (b) If you believe it, it will happen.

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s09_a1 - UNIVERSITY OF WATERLOO School of Computer Science...

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