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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