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! FLASH Lecture: 5.1 exercises
5.1b Derivations I
   flash! 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! 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! FLASH Lecture: 5.3a exercises
   flash! FLASH Lecture: 5.3 mistakes!
5.3a Derivations with rules of replacement I
   flash! 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
Q5.4 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! 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)

Quizzes
 Q5.5a Derived Rules
 Q5.5b Review
Exercises
   flash! 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! FLASH Lecture: 5.6 Strategy
       flash! FLASH Lecture: 5.6 Mistakes to Avoid
  4. Exercises
       flash! FLASH Lecture: 5.6 Strategy
       flash! FLASH Lecture: 5.6 Mistakes to Avoid
       flash! FLASH Lecture: 5.6 exercises: Logical Truth
    5.6a Strategy and Logical Truths
       flash! FLASH Lecture: 5.6 exercises: Logical Equivalence
    5.6b Strategy and Logical Equivalence
       flash! 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

 

Exercises
(these are repeated from the tutorial list above) 

(Selected Answers for some of the problems below.)

5.1a Araucaria Posting
   Flash Guide to Derivations
   flash! FLASH Lecture: 5.1 exercises
5.1b Derivations I
   flash! 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

   flash! 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

   Flashboard on rules of replacement
   flash! FLASH Lecture: 5.3a exercises
   flash! FLASH Lecture: 5.3 mistakes!
5.3a Derivations with rules of replacement I
   flash! 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 easier derivations with rules of replacement

   Flashboard Help for RD
   flash! 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

   flash! 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

   flash! FLASH Lecture: 5.6 Strategy
   flash! FLASH Lecture: 5.6 Mistakes to Avoid
   flash! FLASH Lecture: 5.6 exercises: Logical Truth
5.6a Strategy and Logical Truths
   flash! FLASH Lecture: 5.6 exercises: Logical Equivalence
5.6b Strategy and Logical Equivalence
   flash! FLASH Lecture: 5.6 exercises: Validity
5.6c Strategy and Tests for Validity
5.6d Chapter Review Problems
5.6e Problems for Lecture

5.7a [gold] There are lots here. Start with 5.3. Do as many of these as you'd like, especially toward the end in 5.7 and 5.8. (Rule name changes: use '>E' as the name for MP. If you get beyond 5.3, you'll see some other name changes; just "show rules".)