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

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

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

4. Modus Ponens (M.P)
p q p q

5. Modus Tollens (M.T)
p q q p

6. Hypothetical Syllogism (H.S)
p q
q r
p r

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

8. Constructive Dilemma (C.D)
(p q) (r s) p v r q v s

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

10. Simplification (simp.)
p q p

11. Conjunction (Conj.)
p q p q

12. Addition (Add.)
p p v q

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

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

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

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

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

18. Double Negation (D.N)
p p

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

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

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

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

23. Tautology (Taut)
p (p v p) p (p p)

24. THANK YOU