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
P5.1 Directions to do a 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

1. Complex Derivations and Validity
2. Logical Truth
3. Logical Equivalence
4. 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