Homework 3 Solutions

# t u s p o i g s t u rvnt s

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Unformatted text preview: rniin π T ' ∀i ∀j j i ⇒ π j ¬ ¬ ∨ ψ _ = _ ) ­ ­ a s m _ ∀ :S∙ ∙ ∙< (_⊨ (ϕ )∨ πiπj ­­ sup1 P o i g ( S ⊨ ( U ) T ' ⊨ ◇ψ : rvn T ∃ ϕ ψ)⇒ (S ∃ ) T ◇ψ d f o S⊨ ∃ e f◇ = T ( U ) a e l w S⊨ ∃ Tψ bs a ⇐ S ⊨ ( U ) y a s m _ , t i a h i n h n e n i o d T ∃ ϕ ψ b sup1 hspt sucagdutlψhl. = T ' ⊨ ( U ) S ∃ ϕ ψ P o i g ( S ◇ψ T ( U ) : rvn T'⊨ ∃ )⇒ (S⊨ ∃ ϕ ψ) S ⊨∃◇ψ T' = S ⊨∃π P t s T ) ∃i π i ψ T' :ah(S∙ ∙_⊨ = S ⊨∃π P t s T ) ∃i π i ψ ∧ T' :ah(S∙ ∙_⊨ T = S ⊨∃π P t s T ) ∃i π i ψ ∧ ∀j j i ⇒ π j ¬ ¬ ∨ψ _ = _ ) T' :ah(S∙ ∙_⊨ ( ∙< (_⊨ (ϕ )∨ πiπj) ⇒T ' ∃π P t s T ) ∃i π i ψ ∧ ( j j i ⇒ _ ⊨¬ ¬ ∨ψ ) ∨ ∀j j i ⇒ _ = _ ) S⊨ :ah(S∙ ∙_⊨ (∀ ∙< πj (ϕ ) ( ∙< πiπj) = S ⊨∃π P t s T ) ∃i π i ψ ∧ j j i ⇒ _ ⊨¬ ¬ ∨ψ T' :ah(S∙ ∙_⊨ ∀ ∙< πj (ϕ ) π P t s T ) ∃i π i ψ ∧ j j i ⇒ _ = _ ∨ ∃ :ah(S∙ ∙_⊨ ∀ ∙< πiπj = S ⊨∃(...
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