A Handbook of Set Theoy

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Publisher: Northern Book Centre

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A Handbook of Set Theoy

(Covers the Syllabus of UG & PG Courses of all Indian Universities)

Summary of the Book

The book entitled A Handbook of Set Theory has been written as a textbook for the students of UG and PG.  It begins with the development of the basic concepts of Set, such as, membership, identity, sub-set and proper subset. It then deals with set theoretical operators such as intersection, union, difference and Domain of Universals. Translating everyday language is an integral and essential aspect of logic. Therefore, issues, such as,  the technique of translating everyday language, the concept of consistency and inconsistency, the development of Venn Diagram along with a comparative study between Boolean (or syllogistic) and set theoretical interpretation are incorporated. Elementary Principles about Operations on Set is an integral part of Set Theory as far as application side is concerned. Accordingly, problem relating to this concept has been dealt. Finally, the concept of relation is an integral part of logic. Accordingly, issues, such as, the concept of relations, the concept of ordered couples, the concept of Cartesian or Cross Product, various types of relations with examples are incorporated and elaborately discussed. This book would certainly be useful and effective for the students of Under Graduates (UG) and Post Graduates (PG). The hallmark of this book is that it provides plenty of solving exercises along with an elaborate theoretical background. Therefore, it would be an anticipation of the authors that students who go through this book will immensely be benefitted.


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Book Content

1. General Introduction

Definition of Set
Representation of a Set
Division of Set
Salient Features of Non-empty Set
Technique of Counting the Elements of Set
Basic Concepts of Set
Distinction between 'membership' (Î) and 'identity' (=)
Properties of Sub-set
Comparison between Sub-set and Membership, i.e., (Í) and (Î)
Type of Sets
Summary of the Chapter
Exercises along with Solutions
Suggestive Questions

2. The Empty Set

Empty Set can be the members of Non-empty Set
Reasons or Grounds for admitting Empty-set
Characteristic of Empty Set
Operation on Sets

3. Translating Everyday Language

A Few Exceptions
Technique of Symbolizing Everyday Language
More Solutions
Venn Diagrams
A Few Examples
Consistency and Inconsistency
A Few Examples
Concept of Mutual Exclusive and Mutual Inclusive
Interpretation of sub-set (Í), Proper sub-set (Ì) and Identity (=) by means of Venn Diagram 
Exercises with Solutions
Suggestive Questions

4. On Relations

Ordered Couples
The distinction between a Set and an Ordered Couple
Can more than two objects be accommodated in an Ordered Couple
The Concept of Cross-Product
Definition of Relations
Ordered Couples is a Binary Relation
Can an Ordered Couple be Regarded as a Relation
Some Special Terminology or Attribute of Binary Relation
Exercises along with Solutions
Properties of Binary Relations
Exercises along with solutions
Suggestive Questions

Subject Index

Author / Editors / Contributors


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