This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: = 2 m3 (4 + 2 + 1) = 2 m3 · 7 < 2 m3 · 8 = 2 m3 · 2 3 = 2 m a m < 2 m 7. Prove using strong induction that for any propositional formula P that is in negationnormal form, ¬ P is equivalent to a formula in negationnormal form. Proof by induction on P ≥ NNF i) P ≡ q : ¬ P = ¬ q ∈ NNF by deﬁnition of NNF . P ≡ ¬ q : ¬ P = ¬¬ q = q ∈ NNF by deﬁnition of NNF . ii) Assume that S and T satisﬁes the property. We have S ∈ NNF , ¬ S ≡ S where S ∈ NNF , and T ∈ NNF , ¬ T ≡ T where T ∈ NNF P ≡ S ∧ T : ¬ P ≡ ¬ ( S ∧ T ) ≡ ¬ S ∨ ¬ T ≡ S ∨ T ∈ NNF P ≡ S ∨ T : ¬ P ≡ ¬ ( S ∨ T ) ≡ ¬ S ∧ ¬ T ≡ S ∧ T ∈ NNF 3 P ≡ S → T : ¬ P ≡ ¬ ( S → T ) ≡ ¬ ( ¬ S ∨ T ) ≡ ¬¬ S ∧ ¬ T ≡ S ∧ T ∈ NNF 4...
View
Full Document
 Fall '08
 HAULLGREN
 Logic, Addition, Mathematical Induction, Summation, Natural number

Click to edit the document details