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 to do a 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 Q5.4a 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)

Quizz Q5.5a Derived Rules
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

1. Complex Derivations and Validity
2. Logical Truth
3. Logical Equivalence FLASH Lecture: 5.6 Strategy FLASH Lecture: 5.6 Mistakes to Avoid
4. 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