2. 1

3. 2 Day 1Intro Day 2Chapter 1 Day 3Chapter 2 Day 4Chapter 3 Day 5Chapter 4 Day 6Chapter 4 Day 7Chapter 4 Day 8EXAM #1 40% of Exam 60% of Exam 10 arguments 4 pts each 12 translations 5 pts each

4. 3  if – then  not  or &and

5. 4 necessaryonly if unless-in-which-case …if… if-otherwiseneither-nor …xor… sufficientif and only if unless

6. 5  xor   or , but not both  and  (    ) &  (  &  )  (  &  )  (  &  ) exclusive ‘or’

7. 6 neither  nor  not  and not   &  &    (    ) neither-nor

8. 7  if  if  then       …if…

9. 8 only if ifnot if not then not not  only if  only if  notif not  if not       

10. 9 if and only if (      )&(    )  only if  and  if   if and only if 

11. 10 unless  if not   unless  not  if   thenif not      

12. 11 I will play tennis if it is sunny; otherwise, I will play racketball T if S ; otherwise, R this answers two questions: what will I do if it's sunny? what will I do otherwise (i.e., if it is not sunny)? play tennis play racketball

13. 12 if not S then Randif S then T (  S  R ) & ( S  T ) if it’s not sunny, then I’ll play racketball furthermore if it’s sunny, then I’ll play tennis

14. 13 I will play tennis unless it rains, in which case I will play squash T unless R, in which case S this answers two questions: what will I do unless it rains (i.e., if it does not rain)? what will I do in case it rains (i.e., if it does rain)? play tennis play squash

15. 14 if R then Sandif  R then T ( R  S ) & (  R  T ) if it does rain, then I’ll play squash furthermore if it does not rain, then I’ll play tennis

16. 15 to get an Ain order to take 4 exams necessary it is necessary me to get an Ain order for me to take 4 exams necessary it is necessary for I get an Ain order that I take 4 exams necessary it is necessary that taking 4 exams getting an A necessary is necessary for

17. 16 simplest paraphrase: is necessary for  is necessary for  This amounts to saying if  does not happen, then neither does  if not  then not      

18. 17 is necessary for taking 4 examsE is necessary for getting an AA if E does not happen, then neither does A if not E then not A E  AE  A

19. 18 to get an Ain order to get a hundred sufficient it is sufficient me to get an Ain order for me to get a hundred sufficient it is sufficient for I get an Ain order that I get a hundred sufficient it is sufficient that getting a hundred getting an A sufficient is sufficient for

20. 19 simplest paraphrase: is sufficient for  is sufficient for  This amounts to saying if  does happen, then so does  if  then      

21. 20 is sufficient for getting a hundredH is sufficient for getting an AA if H does happen, then so does A if H then A H  AH  A

22. 21 H getting a hundredH is not necessary for getting an AA you won’t get an A A A not A A ) ) ( ( thenif you don’t get a hundred it is not true that  H H  thenif not H is nec fornot

23. 22 E taking all the examsE is not sufficient for getting an AA you will get an A A A A ) ) ( ( thenif you (merely) take all the exams it is not true that  E  thenif E is suf fornot

24. 23  is necessary for   is sufficient for   is not necessary for   is not sufficient for 

25. 24  is both necessary and sufficient for   is necessary, but not sufficient, for   is sufficient, but not necessary, for   is neither necessary nor sufficient for 

26. 25 averaging (at least) fiftyA is both necessary and sufficient for passingP ( A  P ) A is sufficient for P & and (  A   P ) A is necessary for P

27. 26 taking four examsE is necessary but not sufficient for getting an AA  ( E  A ) E is not sufficient for A & but (  E   A ) E is necessary for A

28. 27 getting a hundredH is sufficient but not necessary for getting an AA  (  H   A ) E is not necessary for A & but ( H  A ) H is sufficient for A

29. 28 attending classA is neither necessary nor sufficient for passingP  ( A  P ) A is not sufficient for P & and  (  A   P ) A is not necessary for P

30. 29