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3. 3 Hx xx x is happythere is some x : who is happythere is someone is happysomeone

4. 4  Hx xx x is not happythere is some x : who is not happythere is someone is unhappysomeone

5. 5 Hx xx x is happyno matter who x is you are happyno matter who you are is happyeveryone

6. 6  Hx xx x is not happyno matter who x is you are not happyno matter who you are is unhappyeveryone

7. 7 Hx xx x is happythere is no x : who is happythere is no one is happyno one

8. 8 Hx xx x is happynot: no matter who x is you are happynot: no matter who you are is happynot everyone

9. 9 some Freshman is Happy Hx&Fx xx x is Handx is Fthere is some x there is someonewho is Handwho is F ()

10. 10 no Freshman is Happy Hx&Fx xx x is Handx is Fthere is no x there is no onewho is Handwho is F ()

11. 11 every Freshman is Happy Hx  Fx xx IF x is FTHENx is Hno matter who x is no matter who you areIF you are FTHENyou are H )(

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13. 13 GENERAL STRATEGY (1)Count the number of quantifiers in original sentence. (2)Determine the overall structure of the sentence. (3)Work on constituents separately. (4)Substitute constituents back into overall formula. (5)Count the number of quantifiers in final formula. (6)Compare (5) with (1).

14. 14 everyone is FRIENDLY, but not everyone is HAPPY  x Hx  x Fx  & everyone is H notbut everyone is F  x Hx  x Fx

15. 15 every CAT is a PET, but not every PET is a CAT  x ( Px  Cx )  x ( Cx  Px )  & every P is C notbut every C is P  x ( Px  Cx )  x ( Cx  Px )

16. 16 if everyone is FRIENDLY, then everyone is HAPPY  xHx  xFx  everyone is Htheneveryone is Fif  xHx  xFx

17. 17 if every STUDENT is FRIENDLY, then every STUDENT is HAPPY  x(Sx  Hx)  x(Sx  Fx)  every S is Hthenevery S is Fif  x(Sx  Hx)  x(Sx  Fx)

18. 18 Basic Principle both ‘any’ and ‘every’ are universal quantifiers, BUT they are usually not inter-changeable.

19. 19 every one can Dance  xDx any one can Dance if I can Dance, then every one can Di   xDx if I can Dance, then any one can

20. 20 no one respects every one if every one can fix your car, then I can Jay doesn’t respect every one is every one here? no one respects any one  if any one can fix your car, then I can  Jay doesn’t respect any one  is any one here? 

21. 21 the scope of ‘every’ is narrow the scope of ‘any’ is wide

22. 22  xRjx not! Jay respects everyone Jay doesn’t respect everyone ‘not’ (  ) has wide scope ‘every’ (  ) has narrow scope 

23. 23 ‘any’ (  ) has wide scope ‘not’ (  ) has narrow scope  Rjx xx Jay does not respect xno matter who x is Jay does not respect youno matter who you are etc.  Rjcno!does Jay respect c?  Rjbno!does Jay respect b?  Rja no!does Jay respect a? Jay doesn’t respect anyone ?Rjc ?Rjb ?Rja

24. 24 Rjx xx Jay respects xthere is no x : whom Jay respectsthere is no one Jay respects no one Recall Jay doesn’t respect anyone = Jay respects no one  x  Rjx =   x Rjx    =   

25. 25 satan winseveryone fails ‘every’ has narrow scope ‘if…then’ has wide scope if everyone fails, then satan wins Ws  xFx  thenif Ws  xFx

26. 26  : Ws (3) As  xFx (2) CD  :  xFx  Ws (1)

27. 27 etc. satan winsthenc failsif satan winsthenb failsif satan winsthena failsif if anyone fails, then satan wins satan winsthenanyone failsif

28. 28 ‘any’ has wide scope ‘if…then’ has narrow scope satan winsthenyou failifno matter who you are satan winsthenx failsifno matter who x is Ws  Fx xx )(

29. 29 UD = Universal Derivation (later!)  : Ws (4) As Fa(3) CD  : Fa  Ws (2) UD  :  x ( Fx  Ws ) (1)

30. 30 Sometimes (but not always) ‘if-any’ = ‘if-some’  x ( Fx   ) =  xFx   provided  has no free occurrence of ‘x’

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