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Strategies - Phil 3 Winter 2008 Strategies for Constructing...

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Phil 3 Winter 2008 Strategies for Constructing Proofs 1. To derive a statement letter or a negation , use Reductio Ad Absurdum. n. p (~ p) Assume . . . . . . . . . m. q • ~ q ------- m+1. ~ p (p) n – m, RAA 2. To derive a conditional , use Conditional Proof. n. p Assume . . Use appropriate strategy to show consequent . m. q ------- m+1. p q n – m, CP 3. To derive a disjunction , derive the conditional to which it is equivalent using Conditional Proof and then use MI to obtain the disjunction. 4. To derive a biconditional , show each conditional separately using Conditional Proof, then conjoin them and use ME to obtain the biconditional. 5. To derive a conjunction , show each conjunct separately by following the appropriate strategy. Then use Conj to obtain the conjunction. 6. Perform MP, MT, and DS whenever possible. 7. If the negation of a conjunction or a disjunction appears on a line, use DeMorgan’s. 8. If the negation of a conditional appears on a line, use MI to turn the conditional into a disjunction and then use DeMorgan’s.
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