Unformatted text preview: S ‘ A for any wﬀ A . (30%) 2. Prove Proposition 1.11.9 in the notes: Let S be any set of wﬀs and A,B any wﬀs. Then: S ∪ { A } ‘ ¬ B iﬀ S ∪ { B } ‘ ¬ A. (40%) 3. (i) Show that ¬ ( A ⇒ B ) ‘ A and ¬ ( A ⇒ B ) ‘ ¬ B (ii) Prove Lemma 1.11.12 in the notes: If ¯ S is a formally consistent and complete set of formulas and ν is the valuation deﬁned by ν ( p i ) = ( 1 , if p i ∈ ¯ S , if p i 6∈ ¯ S, then for any formula A , ν ( A ) = 1 iﬀ A ∈ ¯ S. 1...
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 Spring '09
 InessaEpstein
 Math, Logic, Logical connective, Propositional calculus, Firstorder logic, Metalogic, Wellformed formula, Prove Proposition

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