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3. 3 Exam 1:Sentential LogicTranslations (+) Exam 2:Sentential LogicDerivations Exam 3:Predicate LogicTranslations Exam 4:Predicate LogicDerivations Exam 5:(finals) very similar to Exam 3 Exam 6:(finals) very similar to Exam 4

4. 4 When computing your final grade, four highest scores I count your four highest scores. missedzero (A missed exam counts as a zero.)

5. 5 In predicate logic, every atomic sentence consists of predicate one predicate and subjects one or more “subjects” including subjects, direct objects, indirect objects, etc. subjectsarguments in mathematics “subjects” are called “arguments” (Shakespeare used the term ‘argument’ to mean ‘subject’)

6. 6 is a dog Elle is awake Kay is asleep Jay PredicateSubject

7. 7 Jay is taller than Elle Elle is next to Kay KayrespectsJay ObjectPredicateSubject

8. 8 to from to JayElleprefersKay JayElleboughtKay KayEllesoldJay Indirect Object Direct Object PredicateSubject

9. 9 predicate A predicate is an "incomplete" expression – i.e., an expression with one or more blanks – such that, whenever the blanks are filled by noun phrases, the resulting expression is a sentence. predicatenoun phrase 2 noun phrase 1 sentence

10. 10 connective A connective is an "incomplete" expression – i.e., an expression with one or more blanks – such that, whenever the blanks are filled by sentences, the resulting expression is a sentence. connectivesentence 2 sentence 1 sentence 3

11. 11 is tall is taller than recommendsto

12. 12 Predicatesupper case letters 1.Predicates are symbolized by upper case letters. Subjectslower case letters 2.Subjects are symbolized by lower case letters. Predicatesfirst 3.Predicates are placed first. Subjectssecond 4.Subjects are placed second. Pred sub 1 sub 2 …

13. 13 Kay recommended Elle to Jay Jay recommended Kay to Elle Kay is taller than Elle Jay is taller than Kay Kay is tall Jay is tall R kej R jke T ke T jk TkTk TjTj

14. 14 neither Jay nor Kay is tall both Jay and Kay are tall Jay is not taller than Kay Jay is not tall Jay is taller than both Kay and Elle T jk & T je Tj & TkTj & Tk Tj & TkTj & Tk  T jk TjTj

15. 15 JayandKayare married Jay and Kay are married (individually) = Jayis marriedandKayis married Jay is married, and Kay is married andare married Mj&MkMj & MkMj&MkMj & Mk JayandKayare married Jay and Kay are married (to each other) M jk

16. 16 Quantifiers are linguistic expressions denoting quantity. Examples every, all, any, each, both, either some, most, many, several, few no, neither at least one, at least two, etc. at most one, at most two, etc. exactly one, exactly two, etc.

17. 17 Quantifiers Quantifiers combine common nounsverb phrases common nouns and verb phrases to form sentences. Examples everysenioris happy every senior is happy nofreshmanis happy no freshman is happy at least onejunioris happy at least one junior is happy fewsophomoresare happy few sophomores are happy mostgraduatesare happy most graduates are happy predicate logic treats both common nouns and verb phrases as predicates

18. 18  some, at least one existential quantifier  every, any universal quantifier symbol English expressions official name

19. 19 Actually, they are both upside-down.  backwards ‘E’ A E  upside-down ‘A’

20. 20 Quantifier Phrases are Simply Noun Phrases Jay is happy Kay is happy some one is happy every one is happy subject predicate

21. 21 Quantifier Phrases are Sentential Adverbs

22. 22 some oneis happy there is some onewho is happy there is some one such thathe/she is happy there is some x such thatx is happy xHxxHx there is an x (such that) H x pronunciation

23. 23 every oneis happy every one is such thathe/she is happy whoever you areyou are happy no matter who you areyou are happy no matter who x isx is happy xHxxHx for any x H x pronunciation

24. 24 modern logic takes ‘  ’ to mean at least one which means one or more which means one, or two, or three, or … not if a (counting) number is not one or more it must be zero negationat least one thus, the negation of ‘at least one’ not at least one is ‘not at least one’ none which is ‘none’

25. 25 no oneis happy there is no onewho is happy there is no one such thathe/she is happy there is no x such thatx is happy there is not some x such thatx is happy xHxxHx there is no x (such that) H x pronunciation

26. 26 not every oneis happy not every one is such thathe/she is H it is not true that whoever you areyou are H it is not true that no matter who you areyou are H it is not true that no matter who x isx is H xHxxHx not for any x H x pronunciation

27. 27 supposenot everyone is happy thenthere is someone who is not happy i.e.,there is some x : x is not happy  xHx  x  Hx the converse argument is also valid =

28. 28 supposeno one is happy thenno matter who you are you are not happy i.e.no matter who x is x is not happy  xHx  x  Hx the converse argument is also valid =

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