# sp08L11 - Rules of Inference Addition p-pvq p(p v q...

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2200 5 ¬ Rules of Inference Addition: p ------- p v q p (p v q) Simplification: p ^ q --------- p (p ^ q) p Conjunction: p q ----------- p ^ q ((p) ^ (q)) (p ^ q) Modus Ponens p p q ------------ q (p ^ (p q)) q Modus Tollens ¬ q p q -------------- ¬ p (( ¬ q) ^ (p q)) ( ¬ p)

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Hypothetical Syllogism: p q q r ------------ p r ((p q) ^ (q r)) (p r) Disjunctive Syllogism p v q ¬ p ------------ q ((p v q) ^ ( ¬ p)) q Quantified Statements Universal ( 2200 ) Existential ( 5 ) Instantiation 2200 x P(x) 5 x P(x) -------------------------- ------------------------------------- for any c U, P(c) for some specific c U, P(c) Generalization P(c) for a general c U P(c) for some particular c U ---------------------------- ------------------------------------ 2200 x P(x) 5 x P(x) Consider: “Everyone who has taken COT 3100 has taken a course in computer science”
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sp08L11 - Rules of Inference Addition p-pvq p(p v q...

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