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2. 2 Exam 1Sentential LogicTranslations (+) Exam 2Sentential LogicDerivations Exam 3Predicate LogicTranslations Exam 4Predicate LogicDerivations 6 derivations@ 15 points+ 10 free points Exam 5very similar to Exam 3 Exam 6very similar to Exam 4 Exam 1Sentential LogicTranslations (+) Exam 2Sentential LogicDerivations Exam 3Predicate LogicTranslations Exam 4Predicate LogicDerivations 6 derivations@ 15 points+ 10 free points Exam 5very similar to Exam 3 Exam 6very similar to Exam 4

3. 3 OLD name       –––––     OLD name     –––––       a name counts as OLD precisely if it occurs somewhere unboxed and uncancelled OO II

4. 4 NEW name       –––––    NEW name  :        :    a name counts as NEW precisely if it occurs nowhere unboxed or uncancelled OO UD

5. 5    –––––        –––––      is any formula  is any variable  O  O

6. 6 ; (  &  ) –––––––––    ; (    ) –––––––––  &  &O&O OO

7. 7 DD or  D  UD  SL strategy , , &,  show-strategymain operator

8. 8  :        :    ° ° ° UD ?? must be a NEW name

9. 9  :        :  ° °  DD DD As

10. 10 every F is G ; no G is H / no F is H (12) (13) (14) (10) (11) (15) (9) (8) (7) (6) (5) (4) (3) (2) (1) 8,10, Ga 9,9, Ga   Ha 12,13,  Ha 7, Fa Ha 11,14,  6,6,  (Ga & Ha) 1,1, Fa  Ga 4, Fa & Ha 2,  x  (Gx & Hx) DD  :  As  x(Fx & Hx) DD  :   x(Fx & Hx) Pr   x(Gx & Hx) Pr  x(Fx  Gx) OO  &O OO &O II OO OO OO OO

11. 11 (10) (11) (12) (9) (8) (7) (6) (5) (4) (3) (2) (1) if someone is F, then someone is unH / if anyone is F, then not-everyone is H 9,  Hb 6, Hb 10,11  1,8,  y  Hy 4,  xFx DD  :  As  yHy ID  :   yHy As Fa CD  : Fa    yHy UD  :  x(Fx    yHy) Pr  xFx   y  Hy OO OO OO OO II

12. 12 (10) (9) (8) (7) (6) (5) (4) (3) (2) (1) there is someone whom everyone R’s / everyone R’s someone or other 8,9,  7,  Rab 6, Rab 4,  y  Ray 1,  yRyb DD  :  As   yRay  D (ID)  :  yRay UD  :  x  yRxy Pr  x  yRyx II OO OO OO OO

13. 13 (10) (9) (8) (7) (6) (5) (4) (3) (2) (1) there is someone who R’s no-one / everyone is dis-R’ed by someone or other 8,  Rba 6,  y  Rby 4,  y  Rya 1,   yRby DD  :  As   y  Rya  D (ID)  :  y  Rya UD  :  x  y  Ryx Pr  x   yRxy  Rba (11) 9,10, 7,7,  OO OO OO OO II OO

14. 14 (10) (8) (12) (13) (11) (9) (7) (6) (5) (4) (3) (2) (1) there is someone who R’s every F / every F is R’ed by someone or other 8,8, Fa  Rba 1,  y(Fy  Rby) 4,10, Rba 11,12,  9,9,  Rba 6,  y  Rya DD  :  As   yRya  D (ID)  :  yRya As Fa CD  : Fa   yRya UD  :  x(Fx   yRyx) Pr  x  y(Fy  Rxy) OO OO OO II OO OO

15. 15 (10) (6) (12) (13) (14) (11) (15) (9) (8) (7) (5) (4) (3) (2) (1) there is some F who R’s no-one/ everyone is dis-R’ed by some F or other 7,7,  (Fb &  Rba) 1, Fb &   yRby 10,10, Fb   Rba 11,  Rba 8,12   Rba 9,9,  y  Rby 13,14,    yRby 6,6, Fb 4,  y  (Fy &  Rya) DD  :  As   y(Fy &  Rya)  D (ID)  :  y(Fy &  Rya) UD  :  x  y(Fy &  Ryx) Pr  x(Fx &   yRxy) OO OO  &O OO OO OO II &O OO

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