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2 Exam 1:Sentential LogicTranslations (+) Exam 2:Sentential LogicDerivations Exam 3:Predicate LogicTranslations Exam 4:Predicate LogicDerivations Exam 5:(finals) very similar to Exam 3 Exam 6:(finals) very similar to Exam 4 + + + + When computing your final grade, four highest scores I count your four highest scores. missedzero (A missed exam counts as a zero.)

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4 Hx xx formula x is happythere is some x (s.t.) pronoun variable who is happythere is someoneparaphrase is happysomeone original sentence

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5 Hx xx formula x is happyno matter who x is pronoun variable you are happyno matter who you areparaphrase is happyeveryone original sentence

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6 Hx xx formula x is happythere is no x (s.t.) pronoun variable who is happythere is no oneparaphrase is happyno one original sentence

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7 Hx xx formula x is happynot: no matter who x is pronoun variable you are happynot: no matter who you areparaphrase is happynot everyone original sentence

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8 xHx no-one is happy x Hx someone is un-happy everyone is un-happy x Hx not-everyone is happy xHx = =

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10 some F is un-Hsome one is un-H no F is Hno one is H some F is Hsome one is H every F is un-Hevery one is un-H not-every F is Hnot-every one is H every F is H versus every one is H Specific QuantifierGeneric Quantifier

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11 there is someone who …paraphrase some Freshman is Happyoriginal sentence Hx&Fx xx x is Handx is Fthere is some x there is someonewho is Handwho is F () DON’T FORGET PARENTHESES

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12 there is no one who …paraphrase no Freshman is Happyoriginal sentence Hx&Fx xx x is Handx is Fthere is no x there is no onewho is Handwho is F () DON’T FORGET PARENTHESES

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13 no matter who you are … youparaphrase every Freshman is Happyoriginal sentence Hx Fx xx IF x is FTHENx is Hno matter who x is no matter who you areIF you are FTHENyou are H )( DON’T FORGET PARENTHESES

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14 Rule of Thumb (not absolute) the connective immediately “beneath” a universal quantifier ( ) is usually a conditional ( ) the connective immediately “beneath” an existential quantifier ( ) is usually a conjunction (&) ( ) ( & )

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15 x ( Fx & Hx ) some F is un-H x Hx someone is un-H x ( Fx & Hx ) no F is H xHx no-one is H x ( Fx & Hx ) some F is H xHx someone is H x ( Fx Hx ) every F is un-H x Hx everyone is un-H x ( Fx Hx ) not -every F is H xHx not-everyone is H x ( Fx Hx ) every F is H xHx everyone is H

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16 x ( [ Ax & Bx ] Cx ) every AB is C every AMERICAN BIKER is CLEVER x is an American Biker = x is an American, and x is a Biker x is an AB = [ Ax & Bx ] x ( [ Ax & Bx ] & Cx ) some AB is C some AMERICAN BIKER is CLEVER x ( [ Ax & Bx ] & Cx ) no AB is C no AMERICAN BIKER is CLEVER

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17 allegedcriminal imitationleather expectantmother experiencedsailor smallwhale largeshrimp deerhunter racecardriver baby whale killer dandruff shampoo productivity software woman racecar driver

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18 Bostoniancab driver Bostonianattorney

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19 Compare the following: every Bostonian Attorney is Clever every BA is C vs. every Bostonian and Attorney is Clever every B and A is C

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20 a PetisDogandCatevery it is a Pet THEN it is a Dog and it is a Cat IF for any thing PxPx DxDx&CxCx xx in other words every CAT-DOG is a PET })({

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23 every Cat and Dog is a Pet every Cat and every Dog is a Pet every Cat is a Pet, and every Dog is a Pet & x ( Cx Px ) x ( Dx Px )

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24 every member of the class Cats-and-Dogs is a Pet x ( [ Cx Dx ] Px ) x is a member of the class Cats-and-Dogs, = x is a Cat or x is a Dog = [Cx Dx] to be a member of the class Cats-and-Dogs IS to be a Cat or a Dog no matter who x is if x is a member of the class Cats-and-Dogs, then x is a Pet

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25 only only are only only Citizens are Voters only only Men play NFL football only employees only only members only only cars only only right turn only only only Employees are Allowed only only Members are Allowed only only Cars are Allowed only only Right turns are Allowed examples

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26 only ‘only’ is an implicit double-negative modifier onlyIF only IF notIFnot not IFnot IFnotTHENnot IF not THENnot

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27 only are only if you are , are you (no matter who you are) you are only if you are (no matter who you are) x is only if x is (no matter who x is) x is not if x is not (no matter who x is) if x is not , then x is not (no matter who x is) x ( x x )

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28 only = no non only are no non- are no one who is not is there is no one who is not but who is there is no x ( x is not but x is ) x ( x & x ) x ( x x ) =

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