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# hw2 - L-complete if for each α Γ ‘ L α or Γ ‘ L ¬...

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CISC 404/604 Homework 2 Due on Thursday, March 18, 2010 1. Show a. res (( A B ) ( B C )) (( ¬ C A ) B ). b. { (( A B ) ( C D )) } ‘ res (( A ( C D )) ( B ( C D ))) c. (( ¬ C B ) B ) , ( ¬ C ⇒¬ A ) , (( B ∧ ¬ C ) A ) } ‘ res ( B C ). 2. You may use any of the Theorems/Lemmas/Propositions from the text book up through Proposition 1.12 regarding axiomatic theory L while answering this question. In this ques- tion, Γ is a set of wfs. a. Γ is said to be L-inconsistent if for some wf, α , Γ L α as well as Γ L ¬ α . Show that if Γ is L-inconsistent then for any statement form β , Γ L β . b. We say Γ is
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Unformatted text preview: L-complete if for each α , Γ ‘ L α or Γ ‘ L ¬ α . Assume Γ is L-complete. Show that (i) if Γ ‘ L ( α ⇒ β ) then Γ ‘ L ¬ α or Γ ‘ L β . (ii) if Γ ‘ L ¬ ( α ⇒ β ) then Γ ‘ L α and Γ ‘ L ¬ β . c. Show that if Γ ‘ L α i for 1 ≤ i ≤ n and { α 1 ,...,α n } | = α then Γ ‘ L α . d. Show ‘ L ( A ⇒ B ) ⇒ (( C ⇒ A ) ⇒ ( C ⇒ B )). e. Show that if Γ S { α } ‘ L β then Γ S {¬ β } ‘ L ¬ α . 1...
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