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
   flash! Video Lecture: 5.1 exercises
5.1b Derivations I
   flash! 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

   flash! 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
   flash! Video Lecture: 5.3a exercises
   flash! Video Lecture: 5.3 mistakes!
5.3a Derivations with rules of replacement I
   flash! 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

 

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 
   flash! 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)

Quizz
 Q5.5a Derived Rules
Exercises
   flash! 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
       flash! Video Lecture: 5.6 Strategy
       flash! Video Lecture: 5.6 Mistakes to Avoid
       flash! Video Lecture: 5.6 exercises: Logical Truth
    5.6a Strategy and Logical Truths
       flash! Video Lecture: 5.6 exercises: Logical Equivalence
    5.6b Strategy and Logical Equivalence
       flash! 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

 

Quizzes and Presentations
(these are repeated from the tutorial list above) 

Q5.1 A First Derivation
P5.1 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 Flashboard Reductio
P5.4b Doing a Reductio
 Q5.5a Derived Rules
 Q5.5b Review