AliIybar: Created page with "{| class="wikitable" border="1" |- ! Order ! Rule Name ! Formula |- ! 1 | Modus Ponens (M.P.) | p → q p .: q |- ! 2 | Modus Tollens (M.T.) | p → q ~ q .: ~ p |- ! 3 |..."

2017-02-15T13:28:38Z

Created page with "{| class="wikitable" border="1" |- ! Order ! Rule Name ! Formula |- ! 1 | Modus Ponens (M.P.) | p → q p .: q |- ! 2 | Modus Tollens (M.T.) | p → q ~ q .: ~ p |- ! 3 |..."

New page

{| class="wikitable" border="1"
|-
! Order
! Rule Name
! Formula
|-
! 1
| Modus Ponens (M.P.)
| p → q

p

.: q
|-
! 2
| Modus Tollens (M.T.)
| p → q
~ q

.: ~ p
|-
! 3
| Hypothetical Syllogism (H.S.)
| p → q
q → r

.: p → r
|-
! 4
| Disjunctive Syllogism (D.S.)
| p v q
~ p

.: q
|-
! 5
| Constructive Dilemma (C.D.
| (p → q) ∙ (r → s)
p v r

.: q v s1
|-
! 6
| Absorption (Abs.)
| p → q
.: p → (p∙q)
|-
! 7
| Simplification (Simp.)
| p∙q
.: p
|-
! 8
| Conjunction (Conj.)
| p
q

.: p∙q
|-
! 9
| Addition (Add.)
| p
.: p v q
|-
! 10
| De Morgan’s Theorem (De M.)
| ~ (p∙q) ≡ (~ p v ~ q)
~ (p v q) ≡ (~ p∙~ q)
|-
! 11
| Commutation (Com.)
| (p v q) ≡ (q v p)
(p∙q) ≡ (q∙p)
|-
! 12
| Association (Assoc.)
| [p v (q v r)] [(p v q) v r]
[p∙ (q∙r)] [(p∙q) ∙r]
|-
! 13
| Distribution (Dist)
| [p∙(q v r)] ≡ [(p∙q) v (p∙r)]
[p v (q∙r)] ≡ [(p v q) ∙ (p v r)]
|-
! 14
| Double Negation (D.N.)
| p ≡ ~ ~ p
|-
! 15
| Transposition (Trans.)
| (p → q) ≡ (~ q → ~ p)
|-
! 16
| Material Implication (M. Imp.)
| (p → q) ≡ (~ p v q)
|-
! 17
| Material Equivalence (M. Equiv.)
| (p≡q) ≡ [(p → q) ∙ (q → p)]
(p≡q) [(p∙q) v (~ p ∙ ~ q)]
|-
! 18
| Exportation (Exp.)
| [(p∙q) → r] ≡ [p → (q → r)]
|-
! 19
| Tautology (Taut.)
| p ≡ (p v p)
p ≡ (p∙p)

|}

Rules of Inference - Revision history

AliIybar: Created page with "{| class="wikitable" border="1" |- ! Order ! Rule Name ! Formula |- ! 1 | Modus Ponens (M.P.) | p → q p .: q |- ! 2 | Modus Tollens (M.T.) | p → q ~ q .: ~ p |- ! 3 |..."