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.

(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

P5.1 Directions todoa derivation

Exercises

5.1a Araucaria Posting

Video Guide to Derivations

Video Lecture: 5.1 exercises

5.1b Derivations I

Video 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

Video 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

Video Lecture: 5.3a exercises

Video Lecture: 5.3 mistakes!

5.3a Derivations with rules of replacement I

Video 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

5.3e A little harder! (and the "material" conditional explained)

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

Quizzes and Presentations

Q5.4a RD

P5.4b Doing a Reductio

Exercises

Video Lecture: 5.4 exercises

Flashboard Help for RD

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)

Exercises

Video 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

**Exercises**

Video Lecture: 5.6 Strategy

Video Lecture: 5.6 Mistakes to Avoid

Video Lecture: 5.6 exercises: Logical Truth

5.6a Strategy and Logical Truths

Video Lecture: 5.6 exercises: Logical Equivalence

5.6b Strategy and Logical Equivalence

Video Lecture: 5.6 exercises: Validity

5.6c Strategy and Tests for Validity

5.6d Chapter Review Problems

5.6e Problems for Lecture

Reference

**Chapter Five ****Reference**