1. 2 Exam 1Sentential LogicTranslations (+) Exam 2Sentential LogicDerivations Exam 3Predicate LogicTranslations Exam 4Predicate LogicDerivations 6

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

3 OO Tilde-Universal-Out OO Universal-Out UDUniversal Derivation OO Tilde-Existential-Out OO Existential-Out II Existential-In today day 1 day 2 today day 2 day 1

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

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

6 OO Tilde-Universal Out OO Tilde-Existential-Out

7  is any variable  is any (official) formula not everyone is H –––––––––––––– someone is not H   xHx ––––––  x  Hx     ––––––     example

8  is any variable  is any (official) formula no one is H –––––––––––––– everyone is un H   xHx ––––––  x  Hx     ––––––     example = not anyone is H

9 ; (  &  ) –––––––––    ; (    ) –––––––––  &  &O&O OO

10 (6) (5) (4) (3) (2) (1) not every F is H / some F is un-H 5,  x(Fx &  Hx) 4, Fa &  Ha 3,  (Fa  Ha) 1,  x  (Fx  Hx) DD  :  x(Fx &  Hx) Pr   x(Fx  Hx) II OO OO OO

11 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

12  :        :  ° °  DD DD  is any (official) formula  is any variable As  D is a species of ID

13 (13) (12) (10) (11) (14) (9) (8) (7) (6) (5) (4) (3) (2) (1) 10,11,  Ha  Ha 8, Fa   Ha 9, Fa 12,13,  7, Fa &  Ha 6,6,  (Fa &  Ha) 5,5,  (Fa  Ha) 3,  x  (Fx &  Hx) 1,  x  (Fx  Hx) DD  :  As   x(Fx &  Hx)  D (ID)  :  x(Fx &  Hx) Pr   x(Fx  Hx) OO  &O &O II OO OO OO OO OO

14 (12) (13) (14) (10) (11) (15) (9) (8) (7) (6) (5) (4) (3) (2) (1) 8,8,  (Ga & Ha) 12, Ga   Ha 11,13,  Ha 4,4, Ha 7,9,7,9, Ga 10,14,  Fa 6,6,  x  (Gx & Hx) 1,1, Fa  Ga 2,2, Fa & Ha DD  :  As   x(Gx & Hx)  D (ID)  :  x(Gx & Hx) Pr  x(Fx & Hx) Pr  x(Fx  Gx) OO  &O OO  O OO II &O OO OO

15 (5) (10) (9) (8) (7) (6) (4) (3) (2) (1) 1, Fa  Ga 9,  x(Gx & Hx) 7,8, Ga & Ha 5,6, Ga Ha 4, Fa 2, Fa & Ha DD (…  I)  :  x(Gx & Hx) Pr  x(Fx & Hx) Pr  x(Fx  Gx) OO II &I&I OO &O OO

16 (8) (10) (11) (12) (9) (7) (6) (5) (4) (3) (2) (1) if anyone is F, then everyone is unH / if someone is F, then no one is H 1, Fa   y  Hy 7,8,  y  Hy 10,  Hb 9,11,  5, Hb 3, Fa DD  :  As  yHy DD  :   yHy As  xFx CD  :  xFx    yHy Pr  x(Fx   y  Hy) OO OO OO II OO OO

17 (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

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