Quiz%6%and%7%Chapter%7%&%8%%Note%the%two%versions%A%&%B%Nov.18%2010%Exam%A:%1.%%The%sentence:%%%%%%%%%%%%%%%%%%%%(A%and%B%are%proposiEons)%is%“valid”.%%%%%a)%%True%%%b)%False%Exam%B:%1.%The%sentence%%%%%%%%%%%%%%%%%%%%%%(A%is%a%proposiEon)%is%uns aEsfiable%%%%%%%%%%%%%%%%%%%%%%% %a)%True,%%%b)%False%€ A ∨ ¬B€ A ⇒ ¬AExam%A:%2.%%%%a)%True,%%%%b)%False%Exam%B:%2.%%%%%%%a)%True,%%%b)%False%€ ¬(A ∧ ¬B) ≡ ¬A ∨ B€ ((A ∨ B) ∧ C) ≡ (A ∨ C) ∧ (B ∨ C)Exam%A:%3.%The%expression:%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%is%in%CNF%form.%%%%%%a)%True,%%%%b)%False%Exam%B:%3.%The%clau ses%in%th e%expression:%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%are%all%in%Horn%form.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%a)%True,%%%b)%False%€ (A ∨ B) ∧ C ∧ ¬D€ (A ∨ B) ∧ ¬C ∧ ¬DExam%A:%4.%To%prove%“KB%entails%A”%it%is%sufficient%to%show%that%there%is%no%world%for%which%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%is%TRUE.%%%%a)%True,%%%%b)%False%Exam%B:%4.%To%show%entailment%it%is%sufficient%to%show%that%in%every%world%where%A%is%TRUE,%%%%KB%is%also%TRUE.%%%a)%True,%%%b)%False%€ KB ∧ ¬AExam%A:%1.%%Consi der:%the%expression%in%FOL:%Grade(Brother(Jane)).%In%this%case%“Brother(.)”%represents%a:%%%%%a)%%FuncEon%%%b)%Unary%relaEon%Exam%B:%1.%Consi der%the%following%sentence%in%FOL:%%Real(X)%%%(where%X%is%a%variable).%%%%%%%%%%%%%%%%%%%%%Is%the%syntax%of%the%expression%correct%in%FOL?%%%%%%%%%%%%%%%%%%%%%% %a)%Yes,%%%b)%No%Exam%A:%2.%Does%the%following%sentence%in%FOL%capture%the%English%meaning:%%%“all%bears%have%hair”:%%%%a)%True,%%%%b)%False%Exam%B:%2.%Does%the%following%sentence%in%FOL%capture%the%English%meaning:%%%“there%is%a%bear%that%has%white%hair”:%%%%a)%True,%%%b)%False%€ ∀x, Bear(x) ⇒ Hair(x)€ ∃x, Bear(x) ⇒ Hair(x)Exam%A:%2.%Does%the%following%sentence%in%FOL%capture%the%English%meaning:%%%“%There%is%an%anteater%that%eats%bread”:%%%%a)%True,%%%%b)%False%Exam%B:%2.%Does%the%following%sentence%in%FOL%capture%the%English%meaning:%%%“all%anteaters%eat%ants”:%%%%a)%True,%%%b)%False%€ ∃x, Anteater (x) ⇒ EatBread(x)€ ∀x, Anteaters(x) ∧ EatAnts(x)Exam%A:%2.%%%%%%%a)%True,%%%%b)%False%Exam%B:%2.%%%%%%%a)%True,%%%b)%False%€ A ∧ ¬B ∧ CB ∧ ¬D∴ A ∧ C ∧ ¬D€ (A ∨ ¬B ∨ ¬C) ≡ (B ∧ C ⇒
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