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Direct and Converse Theorems - 1st Edition - ISBN: 9780080098326, 9781483155074

Direct and Converse Theorems

1st Edition

The Elements of Symbolic Logic

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Author: I. S. Gradshtein
Editors: I. N. Sneddon M. Stark S. Ulam
eBook ISBN: 9781483155074
Imprint: Pergamon
Published Date: 1st January 1963
Page Count: 192
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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.

Table of Contents

Prefatory Note

Preface to the English Edition


From the Foreword to the First Edition

Chapter I. Direct and Converse Theorems

§ 1. Introduction: Theorems, Axioms and Definitions

§ 2. Theorems

§ 3. The System of Theorems

§ 4. Sets and Properties

§ 5. Relations between Sets

§ 6. The Representation of the Relations between Sets with the Aid of Diagrams

§ 7. The Converse Theorem

§ 8. Inverse Theorems

§ 9. Reductio ad absurdum

§ 10. Negation

§ 11. Necessary and Sufficient Conditions

§ 12. The Locus of Points

§ 13. The Law of Reciprocity

Chapter II. The Elements of Mathematical Logic

§ 14. Introduction

§ 15. Statements: Their Truth and Falsehood

§ 16. The Composition of Statements

§ 17. Equipollence

§ 18. Equipollent Statements

§ 19. The Various Forms of Converse and Inverse Theorems

§ 20. Always True and Always False Statements

§ 21. Statements about Properties

§ 22. "All" and "There Exists"

Solutions of the Problems Incorporated in the Text


No. of pages:
© Pergamon 1963
1st January 1963
eBook ISBN:

About the Author

I. S. Gradshtein

About the Editors

I. N. Sneddon

M. Stark

S. Ulam

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