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Unformatted text preview: such a conclusion e. Since e is not a tautology, some set of truth values for p and q must make e false. But if r is true, then both the premises (,p) ~ rand r V q are true regardless of the values of p and q. This contradicts e being a valid conclusion for this argument. 8. (a) [BB] p 1\ q is true precisely when p and q are both true. (b) By 8(a), we can replace pl\qby the twopremisesp and q. Using modus ponens, p andp ~ r lead to the conclusion r. Using modus tollens, q and 8 ~ (,q)) lead to the conclusion '8. Finally, 8(a) says we can replace '8 and r with ('8) I\r. 9. By Exercise 8(a), the final premise is equivalent to the list of premises q1. q2, ... ,qn. Now...
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 Summer '10
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 Graph Theory

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