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 DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1. (Ex 8.28) 1 P ↔ ¬ P 2 ⊥ Proof: 1 P ↔ ¬ P 2 P 3 ¬ P ↔ Elim: 1, 2 4 ⊥ ⊥ Intro: 2, 3 5 ¬ P ¬ Intro: 24 6 P ↔ Elim: 1, 5 7 ⊥ ⊥ Intro: 5, 6 2. (Ex 8.38) Give formal proofs of both ( P ∧ Q ) → P and ¬ ( P ∧ Q ) ∨ P . These formulas are equivalent, so the point of this exercise is to show how useful it is to have → . The long way: 5 1 2 ¬ ( ¬ ( P ∧ Q ) ∨ P ) 3 P 4 ¬ ( P ∧ Q ) ∨ P 5 ⊥ 6 ¬ P 7 ¬ P 8 P ∧ Q 9 P 10 ⊥ 11 ¬ ( P ∧ Q ) 12 ¬ ( P ∧ Q ) ∨ P 13 ⊥ 14 ¬¬ P 15 ⊥ 16 ¬¬ ( ¬ ( P ∧ Q ) ∨ P ) 17 ¬ ( P ∧ Q ) ∨ P The short way: 1 2 P ∧ Q 3 P ∧ Elim: 2 4 ( P ∧ Q ) → P → Intro: 23 6...
View
Full Document
 Spring '08
 FITELSON
 September 11 attacks, formal proof, Ex 8.19, Ex 8.24, Ex 8.46

Click to edit the document details