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s09_t01 - UNIVERSITY OF WATERLOO School of Computer Science...

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Unformatted text preview: UNIVERSITY OF WATERLOO School of Computer Science CS245 Logic and Computation Spring 2009 TUTORIAL 1 1. Formalization and consistency. (i) If the dog is barking, then the dog is in the house. (ii) If the dog is in the house, then someone is at the front door unless the dog is not barking. (iii) The dog is barking. (iv) Someone is at the front door. (a) Express the sentences as propositional formula. • b – the dog is barking • h – the dog is in the house • d – someone is at the front door i. b ⇒ h ii. h ⇒ ( d ∨ ¬ b ) iii. b iv. d (b) Is this set of formulas consistent? I.e., is there an interpretation where sentences (i)–(iv) are true? Answer this question using a truth table. Explain. b d h b ⇒ h h ⇒ ( d ∨ ¬ b ) ( b ⇒ h ) ∧ ( h ⇒ ( d ∨ ¬ b )) ∧ b ∧ d T T T T T T C T T F F T F T F T T F F T F F F T F F T T T T F F T F T T F F F T T T F F F F T T F Yes, the set of formulas is consistent (see the row marked with C )....
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This note was uploaded on 01/19/2010 for the course CS 246 taught by Professor Wormer during the Spring '08 term at Waterloo.

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s09_t01 - UNIVERSITY OF WATERLOO School of Computer Science...

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