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rules2 - ⋅(q ⋅ r De Morgan’s(DeM ∼(p v q ∼ p ⋅...

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RULES OF INFERENCE Modus Ponens (MP) Modus Tollens (MT) Conjunction (Conj) p q p q p p q q q ∴∼ p p q Hypothetical Syllogism (HS) Simplification (Simp) Constructive Dilemma (CD) p q p q p q p q q r p q r s p r p v r q v s Disjunctive Syllogism (DS) Addition (Add) p v q p v q p p q p v q q p REPLACEMENT RULES Double Negation (DN) p ∼ ∼ p Commutation (Comm) (p v q) :: (q v p) (p q :: (q p) Contraposition (Contra) (p q) :: ( q p) Tautology (Taut) p :: (p v p) p :: (p p) Association (Assoc) [(p v q) v r] :: [p v (q v r)] [(p q) r] :: [p
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Unformatted text preview: ⋅ (q ⋅ r)] De Morgan’s (DeM) ∼ (p v q) :: ( ∼ p ⋅ ∼ q) ∼ (p ⋅ q) :: ( ∼ p v ∼ q) Exportation (Exp) [(p ⋅ q) ⊃ r] :: [p ⊃ (q ⊃ r 29] Implication (Impl) (p ⊃ q) :: ( ∼ p v q) Equivalence (Equiv) (p ≡ q) :: [(p ⊃ q) ⋅ (q ⊃ p)] (p ≡ q) :: [(p ⋅ q) v ( ∼ p ⋅ ∼ q) Distribution (Dist) [p ⋅ (q v r)] :: [(p ⋅ q) v (p ⋅ r)] [p v (q ⋅ r)] :: [(p v q) ⋅ (p v r)] Absorption (Abs) (p ⊃ q) :: [p ⊃ (p ⋅ q)] Implication Denial (ID) ∼ (p ⊃ q) :: (p ⋅ ∼ q)...
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