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# Class Note for PHIL 110 at UMass(11)

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This 16 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 22 views.

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Date Created: 02/06/15

INTRO LOGIC DAY 06 TRANSLATIONS IN SENTENTIAL LOGIC 2 Schedule for Unit 1 Day 1 Intro Day 2 Chapter 1 Day 3 Chapter 2 40 of 8 arguments Day 4 Chapter 3 Exam 5 pts each Day 5 Chapter 4 60 of 12 translations D 6 Ch t 4 ay ap er Exam 5 pts each Day 7 Chapter 4 Day 8 EXAM 1 T Standard Connectives have special symbols and amp or v not if then a NonStandard Connectives must be paraphrased xor neithernor ifotherwise if unlessinwhichcase only if necessary if and only if sufficient unless NonStandard Connectives 1 exclusive or A xor B A orB but not Aand 23 AVE amp AampB AviBampAampiB NonStandard Connectives 1b exclusive or alternative A xor B A but not B B but not A A amp NB B amp A NonStandard Connectives 2 neithernor neither A nor 2 not A and not B N A amp N B A amp 18 NonStandard Connectives 2b neithernor alternative neither A nor not either A or not A or B N A v B A v 3 NonStandard Connectives 2c recall truthtables RvSRampS FTTT FTFFT FTTF FTFTF FFTT TFFFT TFFF TFTTF NonStandard Connectives 3 if ifB ithhen L B gtJL 10 NonStandard Connectives 3 if ifiB if B then A 11 NonStandard Connectives 4 only if giiyifiB A not if notiB if nofZB then not A 18 gt l 12 NonStandard Connectives 5 if and only if A if and only if B A if B and A only if B jg gt21 amp NB gtN l 13 NonStandard Connectives 6 unless A unless B A if not B A if not B if not B then A 2 gt A 14 if otherwise wi 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 is sunny play tennis what will I do OTHERWISE ie IF it is NOT sunny play racketball 15 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 a T amp S gt R 16 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 ie if it does rain what will I do unless it rains play tennis ie if it does not rain what will I do in case it rains play squash 17 unlessinwhichcase cont if it does not if it does rain rain then I ll furthermore then I ll play play tennis squash if notR then T and if R then S R a T amp R a S 18 Necessary Conditions in orderthat 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 Necessary Conditions cont simplest paraphrase A is necessary for B this amounts to saying if A does not happen then neither does 2 if not A then not B A a 13 Example taking 4 exams E is necessary for getting an A A if E does not happen then neither does A if not E then not A E gt A 21 Sufficient Conditions in orderthat get an A it is sufficient that I get a hundred in order for me to get an A it is sufficient for me to get a hundred in order to get an A it is sufficient to get a hundred getting a hundred is sufficient for getting an A 22 11 Sufficient Conditions cont simplest paraphrase A is sufficient for 2 this amounts to saying if i does happen then so does 2 if A then B AAB 23 Example getting a hundred H is sufficient for getting an A A if H does happen then so does A if H then A HaA 24 12 Negation of Necessity getting a hundred H is NOT necessary for getting an A A not H is nec for A if not H then not A NH gt A H gt A it is not you don t you won t true that If get a H then get an A Negation 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 gt A you E gt A merely it is not take the you will true that If exams then get an A Basic Statements A is necessary for B A is sufficient for B A is not necessary for B A is not sufficient for B 27 Combinations A is both necessary and sufficient for B A is necessary but not sufficient for B A is sufficient but not necessary for B A is neither necessary nor sufficient for B 28 14 Example 1 averaging at least fifty A is both necessary and sufficient for passing P A is necessary for P A P and amp A is sufficient for P A P 29 Example 2 taking four exams E is necessary but not sufficient for getting an A A E is necessary forA E A but amp E is not sufficient forA E A 30 15 Example 3 getting a hundred H is sufficient but not necessary for getting an A A H is sufficient forA H A but amp E is not necessary forA H NA 31 Example 4 attending class A is neither necessary nor sufficient for passing P A is not necessary for P A P and amp A is not sufficient for P A P 32 16

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