Unformatted text preview: p is false, r must be true. Since q V (.r) is true and q is false, r must be false, giving a contradiction. 3. (a) [BB] We analyze with a truth table. There are five rows when the premises are all true and in each case the conclusion is also true. The argument is valid. (b) We analyze with a partial truth table showing the nine situations in which both the premises are true. In every case, the conclusion is true. The argument is valid. p T T F F T T F F p T T T F F F F F F q r T T F T T T F T T F F F T F F F r q T T T F T F T T T F T F F T F F F F pVq p+r T T T T T T F T T F T F T T F T s pAq T T T F F F T F T F F F T F T F F F q+r (PV q) + r T T T T T T T T F F T F F F T T rAs (pAq) + (rAs) T T T T F T T T T T F T F T F T F T * * * * * (c) The second and third premises are p ~ rand r ~ s which together imply p ~ s by the chain rule. Thus the argument becomes pVq p~s qVs...
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 Summer '10
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 Logic, Graph Theory, premises, Modus ponens, Modus tollens, double negation, Argument form

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