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 to do a derivation
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

P5.2 Directions for &E and &I.

   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
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
   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)

   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




Chapter Five Reference