martes, 13 de octubre de 2009

Reglas de inferencia 1

Enrique Arias Valencia


p → q


p → q
¬ q


p → q
q → r
∴p → r


p ∨ q
∴ q


(p → q) ∧ (r → s)

p ∨ r
∴ q ∨ s


(p → q) ∧ (r → s)
¬q ∨ ¬s
∴¬p ∨ ¬r


p ∧ q


∴p ∧ q


∴ p ∨ q


p ∨ q
∴ q ∨ p


p → q
∴ p → (p ∧ q)


¬ (p ∨ q) (¬ p ∧¬ q)
¬ (p ∧q) ≡ (¬p ∨ ¬ q)


¬ (p ∧q) ≡ p → ¬ q
¬ (p → q) ≡ p ∧¬q


p 𠪪p


p ↔ q ≡ (p → q) ∧ (q → p)


p → (q → r) ≡ (p ∧q) → r


p → q ≡ ¬ q → ¬p


[p ∨ (q ∨ r)] ≡ [(p ∨ q) ∨ r]
[p ∧(q ∧r)] ≡ [(p ∧q) ∧r]


[p ∧(q ∨r)] ≡ [[(p ∧q) ∨(p ∧r)]
[p ∨(q ∧r)] ≡ [[(p ∨q) ∧(P ∨r)]


p → q ≡ ¬ p ∨q


p ≡ q ≡ (p → q) ∧ (q → p)
p ≡ q ≡ (p ∧ q) ∨ (¬ p ∧¬ q)


p ≡ p ∨p

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