This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

Front Matter Front Matter (pp. iii) 
Table of Contents Table of Contents (pp. iiiiv) 
FOREWORD FOREWORD (pp. vvi)Y. C. WongThe most striking characteristic of modern mathematics is its greater unity and generality. In modern mathematics, the boundaries between different areas have become obscured; very often, what used to be separate and unrelated disciplines are now special cases of a single one; and, amid these farreaching changes, there have emerged certain basic concepts, notations and terminologies that are of considerable importance and frequent use in a large portion of mathematics.
By 1959, I felt that the time was ripe for this University to introduce into its firstyear mathematics course the most fundamental and the more elementary of these basic concepts,...

PREFACE PREFACE (pp. viiviii)K. T. Leung and Doris L. C. Chen 
PART I 
CHAPTER 1 STATEMENT CALCULUS CHAPTER 1 STATEMENT CALCULUS (pp. 321)By a statement (or a proposition or a declarative sentence) we understand a sentence of which it is meaningful to say that its content is true or false. Obviously, each of the following sentences is a statement:
Geography is a science.
Confucius was a soldier.
Cheung Sam is dead and Lee Sai is in prison.
2 is smaller than 3 and 3 is a prime number.
The steering gear was loose or the driver was drunk.
If John is here, then the book is not his.
Whereas none of the following sentences can be regarded as a statement in the...

CHAPTER 2 SETS CHAPTER 2 SETS (pp. 2242)A fundamental concept in mathematics is that of a set. This concept can be used as a foundation of all known mathematics. In this and the following chapters, we shall develop some of the basic properties of sets. In set theory, we shall be dealing with sets of objects. Here we take objects to be simply the individual things of our intuition and our thoughts. In what follows, objects are referred to by their names, usually letters. Thus in saying ‘an object is denoted by
$ x $ ’ or ‘$ x $ is an object’, we mean that ‘$ x $ ’ is a name of the... 
CHAPTER 3 RELATIONS CHAPTER 3 RELATIONS (pp. 4352)We have seen in Section 2 E that, given any two objects
$ x $ and$ y $ , there is a set$ {x,y} $ which has$ x $ and$ y $ as its only elements. Moreover,$ {x,y} = {y,x} $ ; in other words, the order in which the objects$ x $ and$ y $ appear is immaterial to the construction of the set$ {x,y} $ . For this reason the set$ {x,y} $ is called an unordered pair.Let us recall a wellknown technique used in plane analytic geometry. With respect to a fixed rectangular coordinate system, each point
$ P $ in the plane is uniquely represented by a pair ($ x,y $ ) of numbers... 
CHAPTER 4 MAPPINGS CHAPTER 4 MAPPINGS (pp. 5364)Most readers are familiar with the graphical concept of functions. This involves in general a set
$ A $ of objects called arguments, a set$ B $ of objects called values and an act of associating with each argument in$ A $ a unique value in$ B $ . In elementary calculus, an expression$ y=f(x) $ is used to represent an act of associating with each argument$ x $ (a real number) a unique value$ y $ (also a real number). Within the framework of set theory, this situation can be conveniently formulated by means of relations.Definition 4.1.
$ A $ mapping from (or of or on) a...


SPECIAL SYMBOLS AND ABBREVIATIONS SPECIAL SYMBOLS AND ABBREVIATIONS (pp. 6566) 
LIST OF AXIOMS LIST OF AXIOMS (pp. 6666) 
INDEX INDEX (pp. 6768)