Due: thu 22 jan 2009 10am in the cs245 drop boxes. There are multiple correct answers to some of these questions: (9 marks) express each of the following sentences as a formula in propositional logic. W r where: r it rains, w it is winter. 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. Premise 1: v( (b a)) = not (v(b) imp v(a)) Premise 2: v(b c) = v(b) or v(c) In the above boolean valuation, both evaluate to t: (6 marks) use transformational proof to prove: (a b) (b c) c true. (a b) (b c) c ( (a b) (b c)) c impl. (a b) (b c) c dm. (a b) (b c) c.