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1. 2 Exam 1:Sentential LogicTranslations (+) Exam 2:Sentential LogicDerivations Exam 3:Predicate LogicTranslations Exam 4:Predicate LogicDerivations Exam.

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Presentation on theme: "1. 2 Exam 1:Sentential LogicTranslations (+) Exam 2:Sentential LogicDerivations Exam 3:Predicate LogicTranslations Exam 4:Predicate LogicDerivations Exam."— Presentation transcript:

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2 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 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 4 Hx xx formula x is happythere is some x (s.t.) pronoun  variable who is happythere is someoneparaphrase is happysomeone original sentence

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

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

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

8 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 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

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

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

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

14 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 (&)  (  )  ( & )

15 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

16 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

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

18 18 Bostoniancab driver Bostonianattorney

19 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

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

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23 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 )

24 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

25 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

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

27 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 )

28 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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