Logic - The Drill accompanying Logic: The Laws of Truth by Nicholas J.J. Smith (Princeton University Press, 2012)

318 Pages·2012·1.54 MB·English

by  Nicholas J J Smith

LOGIC
The Drill
Nicholas J.J. Smith and John Cusbert
Copyright(cid:13)c 2012byNicholasJeremyJosefSmithandJohnCusbert
Allrightsreserved
Coverphotograph: AlserStraße,Vienna. (cid:13)c NicholasJ.J.Smith
30May2012: firstpublished.
Preface
The first part of this volume contains all the exercise questions that ap-
pear in Logic: The Laws of Truth by Nicholas J.J. Smith (Princeton Univer-
sity Press, 2012). The second part contains answers to almost all of these
exercises. Both the questions and the answers are a collaborative effort
betweenNicholasJ.J.SmithandJohnCusbert.
OneobvioususeofthisworkisasasolutionsmanualforreadersofLogic:
The Laws of Truth—but it should also be of use to readers of other logic
books. Students of logic need a large number of worked examples and
exercise problems with solutions: the more the better. This volume should
helptomeetthatneed.
After each question, a cross-reference of the form ‘[A p.x]’ appears. This
indicatesthepageonwhichtheanswertothatquestioncanbefound. You
can click on the cross-reference to be taken directly to the answer. Each
answer then contains a cross-reference of the form ‘[Q p.x]’ which leads
back to the corresponding question. Other blue items are also links: for
example, clicking on an entry in the Contents pages takes you directly to
the relevant section, and at the end of each exercise set and each answer
setthereisalinkbacktotheContents.
If you find any errors—or have any other comments or suggestions—
pleaseemailusat:
[email protected]
Thelatestversionofthisworkcanbefoundat:
http://www.personal.usyd.edu.au/~njjsmith/lawsoftruth/
Any significant revisions (e.g. corrections or additions to the exercises or
answers)willbedocumentedonthecopyrightpage.
iii
Contents
Preface iii
Questions
2
1. PropositionsandArguments 2
Exercises1.2.1 2
Exercises1.3.1 3
Exercises1.4.1 3
Exercises1.5.1 4
Exercises1.6.1.1 4
Exercises1.6.2.1 5
Exercises1.6.4.1 5
Exercises1.6.6 6
2. TheLanguageofPropositionalLogic 7
Exercises2.3.3 7
Exercises2.3.5 8
Exercises2.3.8 8
iv
Exercises2.5.1 10
Exercises2.5.3.1 11
Exercises2.5.4.1 11
Exercises2.5.5.1 11
3. SemanticsofPropositionalLogic 13
Exercises3.2.1 13
Exercises3.3.1 14
Exercises3.4.1 14
Exercises3.5.1 15
4. UsesofTruthTables 16
Exercises4.1.2 16
Exercises4.2.1 17
Exercises4.3.1 18
Exercises4.4.1 18
5. LogicalForm 20
Exercises5.1.1 20
Exercises5.2.1 20
Exercises5.3.1 21
Exercises5.4.1 22
Exercises5.5.1 23
v
6. Connectives: TranslationandAdequacy 24
Exercises6.5.1 24
Exercises6.6.3 25
7. TreesforPropositionalLogic 27
Exercises7.2.1.1 27
Exercises7.2.2.1 27
Exercises7.2.3.1 28
Exercises7.3.1.1 28
Exercises7.3.2.1 29
Exercises7.3.3.1 30
Exercises7.3.4.1 30
Exercises7.3.5.1 31
8. TheLanguageofMonadicPredicateLogic 32
Exercises8.2.1 32
Exercises8.3.2 33
Exercises8.3.5 34
Exercises8.4.3.1 35
Exercises8.4.5.1 36
9. SemanticsofMonadicPredicateLogic 38
Exercises9.1.1 38
Exercises9.2.1 39
vi
Exercises9.3.1 39
Exercises9.4.3 40
Exercises9.5.1 43
10. TreesforMonadicPredicateLogic 44
Exercises10.2.2 44
Exercises10.3.8 45
11. Models,Propositions,andWaystheWorldCouldBe 47
12. GeneralPredicateLogic 48
Exercises12.1.3.1 48
Exercises12.1.6 49
Exercises12.1.9 50
Exercises12.2.2 52
Exercises12.3.1 54
Exercises12.4.1 57
Exercises12.5.4 57
13. Identity 58
Exercises13.2.2 58
Exercises13.3.1 60
Exercises13.4.3 61
Exercises13.5.1 63
vii
Exercises13.6.1.1 65
Exercises13.6.2.1 65
Exercises13.6.3.1 66
Exercises13.7.4 66
14. Metatheory 70
Exercises14.1.1.1 70
Exercises14.1.2.1 71
Exercises14.1.3.1 71
15. OtherMethodsofProof 72
Exercises15.1.5 72
Exercises15.2.3 74
Exercises15.3.3 75
16. SetTheory 76
Answers
78
1. PropositionsandArguments 78
Answers1.2.1 78
Answers1.3.1 78
Answers1.4.1 79
Answers1.5.1 79
viii
Answers1.6.1.1 80
Answers1.6.2.1 80
Answers1.6.4.1 80
Answers1.6.6 81
2. TheLanguageofPropositionalLogic 84
Answers2.3.3 84
Answers2.3.5 84
Answers2.3.8 85
Answers2.5.1 87
Answers2.5.3.1 89
Answers2.5.4.1 90
Answers2.5.5.1 90
3. SemanticsofPropositionalLogic 92
Answers3.2.1 92
Answers3.3.1 93
Answers3.4.1 95
Answers3.5.1 98
4. UsesofTruthTables 99
Answers4.1.2 99
Answers4.2.1 102
Answers4.3.1 105
ix