Course Content

Section 1  |  Section 2  |  Section 3  |  Section 4  |  Section 5  |  Section 6  |  Section 7 |  Final |  Syllabus

Section 1

Lectures		Self Tests	Study Guide
1.a	What logic is about?		Concepts: Argument;   Premise;   Conclusion;   Statement; Validity; Soundness;   Inductive Logic;   Deductive Logic;   Conditional;   Antecedent;   Consequent; Modus Ponens Skills: Distinguish validity of an argument from truth of a statement Give the two definitions of validity Identify antecedents and consequents of conditionals correctly using antecedent and consequent indicators: If, Provided that, Should, Results in, Brings about, etc. Be able to translate multiple conditionals by working on one connective at a time, thus ensuring that the results have the correct parenthesis structure. Recognize the conclusion and premises of arguments using premise and conclusion indicators: So, Thus, Therefore, Since, Because, For Complete simple proofs using the rule Arrow Out Reading: Propositional Logic Ch. 1-2 Exercises: Ch. 1: 1 2  Ch. 2: 1 2   3a, b, c,   5 7 8 9 11 Sample questions for Quiz on Section 1
1.b	Validity	Identifying Validity T/F Questions on Validity
1.c	Soundness	Soundness 1 Soundness 2
1.d	Inductive Logic
2.2a	Translating Conditionals	Translating Conditionals Translation Patterns
2.2b	Translating Arguments	Translation Indicators
2.3a	Arrow Out
2.3b	Proofs with Arrow Out	Rule Practice: Arrow Out

Section 1  |  Section 2  |  Section 3  |  Section 4  |  Section 5  |  Section 6  |  Section 7 |  Final |  Syllabus

Section 2

Lectures		Self Tests	Study Guide
3.1	Translating 'and'	Translation Review	Concepts: Ampersand;   Conjunction;   Conjunct;   Subproof Skills: Recognize main connectives of complex formulas. Translate: 'onlyif',  'necessary condition', and 'sufficient condition' Translate such words as: but, however, moreover, although, etc. that mean and. Complete proofs using Arrow and And rules Employ correct strategy for creating subproofs for the Arrow  In rule Calculate dependency lists Reading: Propositional Logic Ch. 3-4 Exercises: Ch. 3: 1a, b, c, f, g, j    2b, d   3b, d            6 7 8 9 12 13 Ch. 4: 1b, c, e, f, g, i, j, n 4a, b, c, d            6 9a 10 13 14 16 Sample questions for Quiz on Section 2
3.2a	Rules for &	Rule Practice More Rule Practice
3.2b	Proof Strategy	Exercise 33b Exercise 34 Exercise 36 Exercise 316 Exercise 33d
3.2c	Main Connectives	Main Connectives 1
4.1	More on Translating Conditionals	Translation Indicators Conditional Translation 1 Conditional Translation 2 Translation Patterns
4.2a	Arrow In
4.2b	Dependency Lists
4.2c	Proof Strategy	Exercise 44a  Exercise 44b Exercise 45 Exercise 48 Exercise p47 Exercise p48 Exercise 414
4.2d	Strategy Review

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Section 1  |  Section 2  |  Section 3  |  Section 4  |  Section 5  |  Section 6  |  Section 7 |  Final |  Syllabus

Section 3

Lectures		Self Tests	Study Guide
5.1a	Translating Not	Negation Translation Scope of the Negation Main Connectives 2	Concepts: Indirect Proof;     Reductio ad Adsurdum;     Standard Contradiction; Disjunction;     Disjunct;     Exclusive or;     Inclusive or;     Dilemma Skills: Accurately diagnose the scope of negation in translating English statements, so as to correctly translate such cases as: it is not both RAINING and SNOWING, it is not RAINING and it is SNOWING, it is not RAINING and it is not SNOWING, WATER is necessary but not sufficient for LIFE Translate 'neither A nor B' and 'A unless B' Construct proofs using the negation rules (Negation In and Negation Out) Be able to translate expressions that mean if and only if: just in case, exactly when, exactly if, but only if, is a necessary and sufficient condition for, etc. Understand an appropriately apply the strategies for the Double Arrow Rules Distinguish between Inclusive and Exclusive Or, and know how to translate these cases Understand and apply the strategies for the Or Rules, especially the Out strategy. That is, when AvB appears in the proof, and your last goal is G, know to set the "missing conditionals" A>G and B>G as new goals, and derive G by Or Out. Reading: Propositional Logic Ch. 5-7 Exercises: Ch. 5: 1a, b, c, e, f, g, j, m    3a, b, c             4 5 8 9 10 12 13 Ch. 6: 1b, d, f, g   2b, c            5 7 9 10 11 12 15 Ch. 7: 1a, b, e, f, j, l, n, p, r   3a, b             4 5 6 8  10 11 13 14 Sample questions for Quiz on Section 3
5.1b	Unless	Unless as if not
5.2a	Negation Rules
5.2b	Strategy	Exercise p64 Exercise p67 Exercise p116 Exercise p70 Exercise 53d Exercise 53a Exercise 53c Exercise 519
5.2c	More on Strategy
5.2d	Strategy Review
5.2e	A Very Hard Problem
6.1	Translating Iff	Translating Iff
6.2	Iff Rules	Exercise 65 Exercise 67 Exercise 612
7.1	Translating Or	Or and Negation Scope In/Exclusive Or Unless as Or
7.2	Or In
7.3a	Or Out
7.3b	Proofs using Or Rules	Exercise p97 Exercise p101e Exercise 79 Exercise 713

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Section 1  |  Section 2  |  Section 3  |  Section 4  |  Section 5  |  Section 6  |  Section 7 |  Final |  Syllabus

Section 4

Lectures		Self Tests	Study Guide
8.1a	Completeness and Consistency	Completeness and Consistency	Concepts: Completeness of Proof Rules;  Consistency of Proof Rules; Derived Rule;     Skills: Know how to demonstrate that a rule is derivable Know the Highly Recommended derived rules Appropriately employ the strategies for using the Highly Recommended rules that is, use AR and DM to simplify sentences with the forms: ~(AvB),  ~(A>B), ~(A&B) Know how to handle a disjunction as a goal by either converting to arrow or using the DeMorgan strategy Be able to complete more difficult proofs Reading: Propositional Logic Ch. 8.1, 8.2, 9.2  (9.1 optional) Exercises: Ch. 8: 2b 4 6 8 9 10 12 13 Ch. 9:  8a, b 9b, f, g 10b, d            11 12 14b, d 15 16 21b, c, i Sample questions for Quiz on Section 4
8.1b	Translation Review	Translation Review
8.2a	Strategy Review
8.2b	Sample Proofs 1
8.2c	Sample Proofs 2
8.2d	Sample Proofs 3	Exercise 89
9.1	Derived Rules	Derived Rules
9.2a	Recommended Rules	DeMorgan's Law Converting from Or to Arrow Converting from And to Arrow Contraposition All Rules
9.2b	Rules that Convert Connectives
9.2c	Less Useful Derived Rules
9.2d	Showing Rules are Derived
9.2e	Showing More Derived Rules
9.2f	Derived Rule Proofs 1	Use the PropLogic Progam that comes with the book to check your solutions to all assigned exercises.
9.2g	Derived Rule Proofs 2
9.2h	Derived Rule Proofs 3

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Section 1  |  Section 2  |  Section 3  |  Section 4  |  Section 5  |  Section 6  |  Section 7 |  Final |  Syllabus

Section 5

Lectures		Self Tests	Study Guide
10.1a	Why Truth Tables?		Concepts: Counterexample Skills: Calculate the truth table for a statement Calculate the truth table for an argument and determine its validity status Know how to apply all the tree rules Construct trees for arguments and diagnose their validity status Reading: Propositional Logic Ch. 10.1, Appendix 4, and "How to Make a Tree" Notes, pp. 17-24 or follow this link. Exercises: With Truth Tables: Ch. 10:  1a 4 5 6 8 With Single Sided Trees: Notes:  Problems 1-5 on p. 25 and 1-4 on p. 26 and Ch. 9: 3 12  Ch. 10:  1c 2-6, 8 10 17 19a 21 24 Sample questions for Quiz on Section 5
10.1b	Calculating Statements	Calculating Truth Values
10.1c	Calculating Tables	Speed Test
10.1d	Calculating Validity	Calculating Validity
10.1e	Tables with more than 3 Variables
11a	(Single Sided) Trees
11b	The Tree Rules	Test on Tree Rules
11c	Checking Validity of an Argument
11d	Review	Complex Tree Rules
11e	Open Branches	Counterexamples
11f	A Harder Example	Finding Mistakes in Trees
11g	Rules for Iff
11h	Summary of the Rules	Tree Rule Summary

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Section 1  |  Section 2  |  Section 3  |  Section 4  |  Section 5  |  Section 6  |  Section 7 |  Final |  Syllabus

Section 6

Lectures		Self Tests	Study Guide
12.1a	Logical Truth		Concepts: Valid (TP);  Logical Truth  (TP); Tautology  (TP);  Contradiction (TP);   Contigent (T);  Entailment (TP);    Equivalence (TP);     Consistency (T)   Skills: Know how to test all concepts listed in Section 6 which are marked with "T" with truth tables and trees. Be able to test all concepts marked "P" with proofs. Be able to distinguish singular from general terms. Especially, be able to diagnose such sentences as "A dog got into the garbage" as general, and "The dog got into the garbage" as singular. Be able to translate simple predicate logic sentences with the forms:  Some A are B; All A are B; No A are B; Not all A are B; Any A is B; Not any A is B; Only As are Bs; None but As are Bs; etc.  (See the Predicate Logic Translation Chart in the course Notes for a more complete list.) Reading: Propositional Logic Ch. 12-13 and Predicate Logic Ch. 2 Exercises: Propositional Logic  Ch. 12: 1 2 4 5 7 9 10 Propositional Logic  Ch. 13: 2 3 4b 6 7 9 Predicate Logic Ch. 2:  1 2 3 4 6 Sample questions for Quiz on Section 6
12.1b	Validity and Conditionals	Test on Validity and Conditionals Logical Truth, Contradiction, and Contingency Methods for Checking These Concepts
12.2	Contradiction
12.3	Contingent
13.1	Validity and Entailment	Entailment and Equivalence Consistency
13.2	Equivalence
13.3	Consistency
13.4	Summary	Concepts in Ch. 13 Review of Ch. 12 and Ch. 13
II2.1a	Predicate Logic
II2.1b	Singular Terms
II2.2	General Sentences and Some
II2.3a	All and No
II2.3b	Only	Predicate Logic Symbolization Predicate Logic Symbolization II
II2.3c	Any

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Section 7

Lectures		Self Tests	Study Guide
II3.1	Universal Out		Concepts: Instance Skills: Complete proofs and trees using the predicate logic rules Universal Out, Existential Out and Quantifier Exchange Order the use of the predicate logic rules properly: 1. Quantifier Exchange 2. Existential Out 3. Universal Out Understand, and avoid breaking, the restriction on the Existential Out rule Reading: Predicate Logic Ch. 3-4 Exercises: Predicate Logic Ch. 3: 1-6, 8-13  do proofs and trees Predicate Logic Ch. 4: 10-15  do proofs and trees Sample questions for Quiz on Section 7
II3.2a	Existential Out
II3.2b	Trees with  Existential Out
II4.2a	Quantifier Exchange	Predicate Logic Rules 1 Predicate Logic Rules 2 Predicate Logic Trees
II4.2b	More on Quantifiers

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