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Sets Advanced Level Pure Mathematics Advanced Level Pure Mathematics Algebra Chapter 2 Sets 2.1 Introduction 2 2.2 Venn Diagrams 3 2.3 Equality of Sets 3 2.4 Subsets 4 2.5 Empty Set and Singleton 5 2.6 Operations on Sets 5 2.7 Number of Elements in a Finite Set 10 Prepared by K. F. Ngai Page 1 2

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Sets Advanced Level Pure Mathematics 2.1 Introduction 1. A set is a collection of definite, distinguishable objects. e.g. { chairs , desks , tables } is a set of furniture. { a , e , i , o , u } is a set of vowels. { 0 , 1 , - 1 , 2 , - 2 , 3 , - 3 , ... } is a set of integers. 2. The objects of a set is called the elements or members of the set. e.g. a , e , i , o and u are the elements of the set of vowels. 3. Expressing a set in two ways: (a) Tabular form : e.g. { a , e , i , o , u } is the set of vowels. e.g. {0 , 2 , - 2 , 4 , - 4 , ...} is a set containing all the even numbers. (b) Set-Builder form : e.g. { x : x is a vowels } is the set of vowels. e.g. { x : x is an even number } is a set containing all the even numbers. 4. If x is a member of a set A , we write x A. If x is not belong to a set A , we write x A. e.g. If A = { x : x is a vowel } , then a A , u A , but g A. e.g. If B = { x : x is an integer greater than 11 } , then 20 B , 999 B , but 11 B. 5. Sets containing finite number of objects are called finite sets . Otherwise, it is called an infinite set . e.g. { x : x is a vowel } is a finite set. e.g. { x : x is an integer greater than 11 } is a infinite set. 6. Some symbols are frequently adopted: Prepared by K. F. Ngai Page 2
Sets Advanced Level Pure Mathematics 1. N denoted the set of all positive integers. N = { 1, 2, 3, 4, ... } 2. Z denoted the set of all integers. Z = { 0, 1, - 1, 2, - 2, ... } 3. Q = { p q : p, q Z and q 0 } is the set of rational numbers.

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