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Unformatted text preview: f ⊆ Γ, Γ f  = B . (II) If every ﬁnite subset of Γ is satisﬁable then Γ is satisﬁable. (i). (5 points) Show that if (I) holds then (II) holds. (ii). (5 points) show that if (II) holds then (I) holds. 4. Γ is said to be maximally satisﬁable if Γ is satisﬁable and for any B 6∈ Γ, Γ S {B} is unsatisﬁable. Assume Γ is maximally satisﬁable. a. (7 points) Show that if Γ  = B then B ∈ Γ. b. (8 points) Show that if ( B ∧ C ) ∈ Γ then B ∈ Γ and C ∈ Γ. c. (5 points) (for 604 students only) Assume Γ is a maximally satisﬁable set. Show that for any formula B , B ∈ Γ if and only if ¬B 6∈ Γ. 1...
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This document was uploaded on 12/07/2011.
 Spring '09

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