E-Book, Englisch, 192 Seiten, Web PDF
Gradshtein / Sneddon / Stark Direct and Converse Theorems
1. Auflage 2014
ISBN: 978-1-4831-5507-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
The Elements of Symbolic Logic
E-Book, Englisch, 192 Seiten, Web PDF
ISBN: 978-1-4831-5507-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Direct and Converse Theorems: The Elements of Symbolic Logic, Third Edition explains the logical relations between direct, converse, inverse, and inverse converse theorems, as well as the concept of necessary and sufficient conditions. This book consists of two chapters. The first chapter is devoted to the question of negation. Connected with the question of the negation of a proposition are interrelations of the direct and converse and also of the direct and inverse theorems; the interrelations of necessary and sufficient conditions; and the definition of the locus of a point. The second chapter explains several questions of mathematical logic-a science that is being developed in connection with the theory of mathematical proof. This edition is provided with a large number of problems and questions to help easily understand the material. The book is intended for students studying mathematics, specifically at intermediate colleges of various types. The text is also a useful reference for university students and teachers.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Direct and Converse Theorems: The Elements of Symbolic Logic;6
3;Copyright Page;7
4;Table of Contents;8
5;Prefatory Note;10
6;PREFACE TO THE ENGLISH EDITION;12
7;INTRODUCTION;14
8;FROM THE FOREWORD TO THE FIRST EDITION;17
9;CHAPTER I. DIRECT AND CONVERSE THEOREMS;20
9.1;1. Introduction;20
9.2;2. Theorems;23
9.3;3. The System of Theorems;26
9.4;4. Sets and Properties;28
9.5;5. Relations between Sets;33
9.6;6. The Representation of the Relations between Sets with the Aid of Diagrams;38
9.7;7. The Converse Theorem;44
9.8;8. Inverse Theorems;60
9.9;9. Reductio ad absurdum;65
9.10;10. Negation;76
9.11;11. Necessary and Sufficient Conditions;79
9.12;12. The Locus of Points;82
9.13;13. The Law of Reciprocity;92
10;CHAPTER II. THE ELEMENTS OF MATHEMATICAL LOGIC;98
10.1;14. Introduction;98
10.2;15. Statements: Their Truth and Falsehood;102
10.3;16. The Composition of Statements;110
10.4;17. Equipollence;119
10.5;18. Equipollent Statements;122
10.6;19. The Various Forms of Converse and Inverse Theorems;135
10.7;20. Always True and Always False Statements;139
10.8;21. Statements about Properties;146
10.9;22. "All" and "There Exists";151
11;SOLUTIONS OF THE PROBLEMS INCORPORATED IN THE TEXT;160
