CS245 Lecture : Assignment #2 + Solution Winter 2009

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Due: thu 29 jan 2009 10am in the cs245 drop boxes. There may be multiple correct answers to some of these questions: (25 marks) for each of the following problems, determine whether the argument is valid or invalid. If it is valid, prove its validity using the indicated proof method (natural deduction or semantic tableaux). If it is invalid, provide a counterexample and demonstrate that the argument is invalid. (a) natural deduction: (c d), a b c, (c d) a b c. E 2, 4 b d c d false c c d false assumption. E 1, 11 false cases 5, 6 9, 10 12. 1 (b) natural deduction: ( c b) a. C a b c premise assumption. I 2 7 (c) natural deduction: 7 a b false a a c. 9 (d) semantic tableaux: (c d) a, d a. A counterexample is: v(a) = t, v(c) = t, v(d) = f.

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