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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...
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This note was uploaded on 09/19/2011 for the course PHILOS 12A taught by Professor Fitelson during the Spring '08 term at Berkeley.
 Spring '08
 FITELSON

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