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# Class Note for PHIL 110 at UMass(7)

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This 7 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Massachusetts taught by a professor in Fall. Since its upload, it has received 14 views.

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Date Created: 02/06/15

INTRO LOGIC DAY 06 TRANSLATIONS IN SENTENTIAL LOGIC 2 Standard Connectives have special symbols and amp or v not if then Schedule for Unit 1 Day 1 Intro Day 2 Chapter 1 Day 3 Chapter 2 Day 4 Chapter 3 Day 5 Chapter 4 Day 6 Chapter 4 Day 7 Chapter 4 Day 8 EXAM 1 40 of 10 arguments Exam 4 pts each 60 of 12 translations Exam 5 pts each T NonStandard Connectives must be paraphrased I neithernor I I ifotherwise I I if I I unlessinwhichcase I I only if I I necessary I I if and only if I I suf cient I NonStandard Connectives 1 NonStandard Connectives 3 exclusive or if AxorB AifB Aor B but not bothAandB ithhenA AvBampAampB 3 1 AampBVBampA NonStandard Connectives 2 NonStandard Connectives 4 neithernor only if neither A nor B J14 guy if 3 not A and not B NAampNB notA If noth 5 if nofTB then not A A v B B a A NonStandard Connectives 5 if and only if A if and only if B AifB and A onlyifB BaA amp BaA NonStandard Connectives 6 unless A unless B A if not B A if not B if not B then A B a A 10 ifotherwise 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 it39s sunny play tennis what will I do otherwise ie if it is not sunny play racketball 11 if otherwise cont if it s sunny if it s not then I ll play furthermore sunny then I ll tennis play racketball if S then T and if not 8 then R S T amp S R 12 unessin which case 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 ie if it does not rain what will I do in case it rains ie if it does rain play tennis play squash Necessary Conditions in order that get an A it is necessary that I take 4 exams in order for me to get an A it is necessary for me to take 4 exams in order to get an A it is necessary to take 4 exams taking 4 exams is necessary for getting an A 13 15 unlessinwhichcase cont if it does not if it does rain rain then I ll furthermore then I ll play play tennis squash if R then T and if R then S R T amp R S 14 Necessary Conditions cont simplest paraphrase A is necessary for B This amounts to saying if A does not happen then neither does B if not 54 then not B JZl gtB 16 Example Sufficient Conditions cont taking 4 exams E simplest paraphrase is necessary for A is sufficient for B getting an A A This amounts to saying if E does not happen 39f d h then neitherdoesA 399 095 appeni if not E then not A then so does B if A then B E gt A A gt B 17 Sufficient Conditions Example in order that I get an A getting a hundred H it is sufficient that I get a hundred 395 suf clent for getting an A A In order for me to get an A if H does happen it is sufficient for me to get a hundred then so does A In order to get an A if H then A it is sufficient to get a hundred H gt A getting a hundred is sufficient for getting an A 18 Negations Of Necessity Basic Statements A is necessary for B A is suf cient for B A is not necessary for B A is not suf cient for B 23 getting a hundred H is not necessary for getting an A A not H is nec for A if not H then not A H a A it is not if you don t then you won t true that get a get an A hundred 21 Negations of Sufficiency taking all the exams E is not sufficient for getting an A A not E is suf for A if E then A E a A it is not ifyou then you will true that merely get an A take all the exams 22 Combinations A is both necessary and suf cient for B A is necessary but not suf cient for B A is sufficient but not necessary for B A is neither necessary nor suf cient for B 24 Example 1 averaging at least fifty A is both necessary and suf cient for passing P A is necessary for P NA gt NP and amp A is suf cient for P A gt P 25 Example 2 taking four exams E is necessary but not suf cient for getting an A A E is necessary forA NE gt NA but amp E is not sufficient for A NE gtA 26 Example 3 getting a hundred H is suf cient but not necessary for getting an A A H is sufficient for A H gt A but amp E is not necessary for A N NH gt NA 27 Example 4 attending class A is neither necessary nor sufficient for passing P A is not necessary for P N NA gt NP and amp A is not suf cient for P N A gt P 28

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