WESTERN LOGIC Presented by Malini Sen Assistant Professor

WESTERN LOGIC Presented by Malini Sen Assistant Professor Department of Philosophy Maheshtala College B. B. T. Road. Kolkata - 700141

FORMAL PROOF OF VALIDITY 1) RULES OF INFERENCE 2) RULES OF REPLACEMENT

RULES OF INFERENCE 1) 2) 3) 4) 5) 6) 7) 8) 9) Modus Ponens (M. P) Modus Tollens (M. T) Hypothetical Syllogism (H. S) Disjunctive Syllogism (D. S) Constructive Dilemma (C. D) Absorption (Abs. ) Simplification (simp. ) Conjunction (Conj. ) Addition (Add. )

Modus Ponens (M. P) p p q q

Modus Tollens (M. T) p q q p

Hypothetical Syllogism (H. S) p q r r

Disjunctive Syllogism (D. S) p v q p q

Constructive Dilemma (C. D) (p q) (r s) pvr qvs

Absorption (Abs. ) p q p (p q)

Simplification (simp. ) p q p

Conjunction (Conj. ) p q

Addition (Add. ) p pvq

RULES OF REPLACEMENT 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) De Morgan’s theorem (De. M. ) Commutation (Com. ) Association (Assoc. ) Distribution (Dist. ) Double Negation (D. N) Transposition (Trans. ) Material Implication (Impl. ) Material Equivalence (Equiv. ) Exportation (Exp. ) Tautology (Taut).

De Morgan’s Theorem (De. M. ) (p q) ( p v q) ( p q)

Commutation (Com. ) (p v q) (p q) (q v p) (q p)

Association (Assoc. ) [p v (p v q)] [(p v q) v r] [p (p q)] [(p q) r]

Distribution (Dist. ) [p (q v r)] [(p q) v (p r) [p v (p r)] [(p v q) (p v r)]

Double Negation (D. N) p p

Transposition (Trans. ) (p q) ( q p)

Material Implication (Impl. ) (p q) ( p v q)

Material Equivalence (Equiv. ) (p (p q) q) [(p q) (q p)] [(p q) v ( p q)]

Exportation (Exp. ) (p q) r ] [p (q r)]

Tautology (Taut) p p (p v p) (p p)

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