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Logic Chapter 7 study AP

# Logic Chapter 7 study AP - modus ponens(MP ~F(G H ~F GH...

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modus ponens (MP) ~F (G ≡ H) (A v B) ~(C D) K L ~F (A v B) (K L) (R S) G ≡ H ~(C D) (R S) modus tollens (MT) (D v F) K ~G ~(M v N) ~T ~K ~~(M v N) (H v K) T ~(D v F) ~~G ~(H v K) hypothetical syllogism (HS) A (D F) ~M (R S) (D F) ~H (C v K) ~M A ~H (C v K) (R S) disjunctive syllogism (DS) U v ~(W X) ~(E v F) ~U (E v F) v (N K) ~(W X) (N K) Simplification (Simp) Constructive Dilemma (CD) P · Q (P Q) · (R S) P P v R Q v S Addition (Add) Conjunction (Conj) P P P v Q Q P · Q Commutativity (Com) DeMorgan’s Rule (DM) (p v q) :: (q v p) ~(p · q) :: (~p v ~q) (p · q) :: (q · p) ~(p v q) :: (~p · ~q) Associativity (Assoc) Distribution (Dist) [p v (q v r)] :: [(p v q) v r] [p · (q v r)] :: (p · q) v (p · r) [p · (q · r)] :: [(p · q) · r] [p v (q · r)] :: (p v q) · (p v r)

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Double Negation (DN) p :: ~~p Material Implication (Impl) (A B) :: (~A v B) Material Equivalence (Equiv) (A ≡ B) :: (A B) · (B A) (A ≡ B) :: (A · B) v (~A · ~B) Exportation (Exp) [(A · B) C] :: [A (B C)] Tautology (Taut) A :: (A v A) A :: (A · A) Indirect Proof
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Logic Chapter 7 study AP - modus ponens(MP ~F(G H ~F GH...

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