Summary of Rules - q) 11. Associativity (Assoc) [p (q r)]...

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Rules of implication 1. Modus ponens (MP) p q p q 5. Constructive dilemma (CD) (p q) (r s) p r q s 2. Modus tollens (MT) p q ~q ~p 6. Simplification (Simp) p q p 3. Hypothetical syllogism (HS) p q q r p r 7. Conjunction (Conj) p q p q 4. Disjunctive syllogism (DS) p q ~p q 8. Addition (Add) p p q Rules of Replacement 9. DeMorgan’s rule (DM) ~(p q) :: (~p ~q) ~(p q) :: (~p ~q) 14. Transposition (Trans) (p q) :: (~q ~p) 10. Commutativity (Com) (p q) :: (q p) (p q) :: (q p) 15. Material implication (Impl) (p q) :: (~p
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Unformatted text preview: q) 11. Associativity (Assoc) [p (q r)] :: [(p q) r] [p (q r)] :: [(p q) r] 16. Material equivalence (Equiv) (p q) :: [(p q) (q p)] (p q) :: [(p q) (~p ~q)] 12. Distribution (Dist) [p (q r)] :: [(p q) (p r)] [p (q r)] :: [(p q) (p r)] 17. Exportation (Exp) [(p q) r] :: [p (q r)] 13. Double negation (DN) p :: ~~p 18. Tautology (Taut) p :: (p p) p :: (p p) 1...
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