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# Direct and Converse Theorems : the Elements of Symbolic Logic.

Author: I S Gradshtein; I N Sneddon; M Stark; S Ulam Burlington : Elsevier Science, 2014. International series of monographs in pure and applied mathematics. eBook : Document : EnglishView all editions and formats 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 chap.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version:Gradshtein, I.S.Direct and Converse Theorems : The Elements of Symbolic Logic.Burlington : Elsevier Science, ©2014 Document, Internet resource Internet Resource, Computer File I S Gradshtein; I N Sneddon; M Stark; S Ulam Find more information about: I S Gradshtein I N Sneddon M Stark S Ulam 9781483155074 1483155072 898771774 1 online resource (192 pages). Front Cover; Direct and Converse Theorems: The Elements of Symbolic Logic; Copyright Page; Table of Contents; Prefatory Note; PREFACE TO THE ENGLISH EDITION; INTRODUCTION; FROM THE FOREWORD TO THE FIRST EDITION; CHAPTER I. DIRECT AND CONVERSE THEOREMS; 1. Introduction; 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 ReciprocityCHAPTER 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. International series of monographs in pure and applied mathematics.

### Abstract:

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 chap.

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