Chapter Five:

Deductions for Sentence logic

In this chapter, we do formal deductions: a kind of proof procedure. We will call these step-by-step arguments "derivations". For example, one step might be an application of DS and the second of MT. So, long as each step of the is valid, the whole "chain" of reasoning is valid.

Tutorials

(Selected Answers for some of the exercise problems below.)

**Tutorial One:** **Derivations with MP, MT, and DS **

Quizzes and Presentations

Q5.1 A First Derivation

P5.1a Flash Guide to Derivations

P5.1b Directions todoa derivation

Exercises

5.1a Araucaria Posting

Flash Guide to Derivations

FLASH Lecture: 5.1 exercises

5.1b Derivations I

FLASH Lecture: 5.1c exercises

5.1c Derivations II

5.1d Derivations III

5.1e Derivations IV

5.1f Derivations for Lecture

5.1g More Derivations for Lecture

**Tutorial Two:** Trusting our rules: &I and &E

Presentation

P5.2 Directions again...now for &E and &I.

Exercises

FLASH Lecture: 5.2 exercises

5.2a Derivations with &E and &I

5.2b More Derivations

5.2c Yet More Derivations

5.2d Derivations and a little strategy

5.2e A Few More Derivations

**Tutorial Three:** Rules of Replacement: DM, DN, IM, EQ

Flashboard on rules of replacement

FLASH Lecture: 5.3a exercises

FLASH Lecture: 5.3 mistakes!

5.3a Derivations with rules of replacement I

FLASH Lecture: 5.3b exercises

5.3b Derivations with rules of replacement II

5.3c More derivations with just DM and DN

5.3d More and easier derivations with rules of replacement

**Tutorial Four:** Reductio ad Absurdum: RD

Quizzes and Presentations

Q5.4 RD

Q5.4b General Quiz on 5.1-5.4

P5.4a Flash Reductio

P5.4b Doing a Reductio

Exercises

Flashboard Help for RD

FLASH Lecture: 5.4 exercises

5.4a Derivations with RD I

5.4b Derivations with RD II

5.4c Derivations with RD III

5.4d More RD for class

5.4e Yet More RD

5.4f RD for deriving rules

**Tutorial Five:** Derived rules: Helpful, short-cut rules (but not essential)

Quizzes

Q5.5a Derived Rules

Q5.5b Review

Exercises

FLASH Lecture: 5.5 exercises

5.5a Deriving Rules I

5.5b Deriving Rules II

5.5c Using the Derived Rules I

5.5d Deriving Rules III

5.5e Using the Derived Rules II

5.5f Practice for class

5.5g More practice for class

5.5h Using the Derived Rules III

**Tutorial Six:** Putting it all together

- Complex Derivations and Validity
- Logical Truth
- Logical Equivalence

FLASH Lecture: 5.6 Strategy

FLASH Lecture: 5.6 Mistakes to Avoid

**Exercises**

FLASH Lecture: 5.6 Strategy

FLASH Lecture: 5.6 Mistakes to Avoid

FLASH Lecture: 5.6 exercises: Logical Truth

5.6a Strategy and Logical Truths

FLASH Lecture: 5.6 exercises: Logical Equivalence

5.6b Strategy and Logical Equivalence

FLASH Lecture: 5.6 exercises: Validity

5.6c Strategy and Tests for Validity

5.6d Chapter Review Problems

5.6e Problems for Lecture

**Tutorial Seven:** [gold] Conditional Proof and Difficult Derivations

Reference

**Chapter Five ****Reference**

Quizzes and Presentations

(these are repeated from the tutorial list above)

Q5.1 A First Derivation

P5.1a Flash Guide to Derivations

P5.1b Directions to *do* a derivation

P5.2 Directions again...now for &E and &I.

Q5.4 RD

Q5.4b General Quiz on 5.1-5.4

P5.4a Flash Reductio

P5.4b Doing a Reductio

Q5.5a Derived Rules

Q5.5b Review

Exercises

(these are repeated from the tutorial list above)

(Selected Answers for some of the problems below.)

5.1a Araucaria Posting

Flash Guide to Derivations

FLASH Lecture: 5.1 exercises

5.1b Derivations I

FLASH Lecture: 5.1c exercises

5.1c Derivations II

5.1d Derivations III

5.1e Derivations IV

5.1f Derivations for Lecture

5.1g More Derivations for Lecture

FLASH Lecture: 5.2 exercises

5.2a Derivations with &E and &I

5.2b More Derivations

5.2c Yet More Derivations

5.2d Derivations and a little strategy

5.2e A Few More Derivations

Flashboard on rules of replacement

FLASH Lecture: 5.3a exercises

FLASH Lecture: 5.3 mistakes!

5.3a Derivations with rules of replacement I

FLASH Lecture: 5.3b exercises

5.3b Derivations with rules of replacement II

5.3c More derivations with just DM and DN

5.3d More easier derivations with rules of replacement

Flashboard Help for RD

FLASH Lecture: 5.4 exercises

5.4a Derivations with RD I

5.4b Derivations with RD II

5.4c Derivations with RD III

5.4d More RD for class

5.4e Yet More RD

5.4f RD for deriving rules

FLASH Lecture: 5.5 exercises

5.5a Deriving Rules I

5.5b Deriving Rules II

5.5c Using the Derived Rules I

5.5d Deriving Rules III

5.5e Using the Derived Rules II

FLASH Lecture: 5.6 Strategy

FLASH Lecture: 5.6 Mistakes to Avoid

FLASH Lecture: 5.6 exercises: Logical Truth

5.6a Strategy and Logical Truths

FLASH Lecture: 5.6 exercises: Logical Equivalence

5.6b Strategy and Logical Equivalence

FLASH Lecture: 5.6 exercises: Validity

5.6c Strategy and Tests for Validity

5.6d Chapter Review Problems

5.6e Problems for Lecture

5.7a [gold] There are lots here. Start with 5.3. Do as many of these as you'd like, especially toward the end in 5.7 and 5.8. (Rule name changes: use '>E' as the name for MP. If you get beyond 5.3, you'll see some other name changes; just "show rules".)