LCA Textbook for Ventura College - The Logic Course Adventure

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LCA Textbook for Ventura College

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19. I ♥ Formal Proofs, PROP 6 Sections

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19.1 -> Conclusions: Awesome!

19.2 -> Premises: Be Patient

19.3 The Contradiction Trick

19.4 The Reiteration Trick

19.5 Biconditional: Twice the Work

19.6 Extra Practice

20. Metalogic 6 Sections

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20.2 Proving Soundness

20.3 Truth-Functional Completeness (TFC)

20.4 More TFC

20.5 Nor and Nand

20.6 Extra Practice

20.1 Soundness and Completeness

21. Welcome to FOL 5 Sections

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21.1 Terms: Names and Variables

21.2 Predicates: Properties and Relations

21.3 The Identity Predicate =

21.4 Atomic Sentences

21.5 Extra Practice

22. Meet the Quantifiers 4 Sections

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22.1 All (A) and Exists (E)

22.2 Variables, Free and Bound

22.3 Well-Formed Formulas vs. Sentences

22.4 Extra Practice

23. Semantics of FOL 4 Sections

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23.1 Names and Objects

23.2 The Domain

23.3 Predicates and Intended Interpretations

23.4 Extra Practice

24. Aristotelian Forms 5 Sections

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24.1 Four Aristotelian Forms

24.2 Advanced Forms

24.3 Vacuous Generalizations

24.4 Pairs of Contradictories

24.5 Extra Practice

25. FO Equivalences 7 Sections

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25.1 DeMorgan’s for Quantifiers (DeMQ)

25.2 Null Quantification (Null)

25.3 Variable Switch (VS)

25.4 Distribution for Quantifiers (Dist)

25.5 Prenex Form and Chain of Equivalences

25.6 Quantifier Reorder (QR)

25.7 Extra Practice

26. FO Necessities 5 Sections

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26.1 FO Validities

26.2 FO Falsities

26.3 Truth-Functional Form Algorithm (TFFA)

26.4 The Chart

26.5 Extra Practice

27. FO Counterexamples 2 Sections

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27.1 Counterexamples in FOL

27.2 Extra Practice

28. Multiple Quantifiers 3 Sections

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28.1 Same Quantifiers

28.2 Mixed Quantifiers

28.3 Extra Practice

29. Numerical Quantification 5 Sections

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29.1 “At least”

29.2 “At most”

29.3 “Exactly”

29.4 Definite Descriptions: “The”

29.5 Extra Practice

30. Proofs in FOL: 2 Easy Rules 4 Sections

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30.1 Simple Informal Proofs

30.2 EIntro: Existential Generalization

30.3 AElim: Universal Instantiation

30.4 Extra Practice

31. Proofs in FOL: 2 Hard Rules 5 Sections

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31.1 Universal Generalization

31.2 AIntro

31.3 Existential Instantiation

31.4 EElim

31.5 Extra Practice

32. = Proofs in FOL 3 Sections

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32.1 =Elim

32.2 =Intro

32.3 Extra Practice

33. I ♥ Formal Proofs, FOL 6 Sections

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33.1 Universals Are Easy

33.2 Existentials Are Harder

33.3 Key Pattern ~ExP(x)

33.4 Annoying Pattern ~AxP(x)

33.5 Regular Routine for Quantifiers

33.6 Extra Practice

34. Logic and Set Theory 5 Sections

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34.1 Sets and Membership

34.2 Cardinality = Size

34.3 Natural Numbers and Infinite Sets

34.4 1-to-1 Correspondence, Transfinite Arithmetic

34.5 Extra Practice

35. Logic and Infinity 4 Sections

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35.1 E, O, and Z

35.2 The Rational Numbers Q

35.3 The Real Numbers R

35.4 Extra Practice

36. Ch. 17-35 Review 2 Sections

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36.1 Terminology Review

36.2 Review Problems

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