Sets Definition A collection of well defined objects

Sets Definition: A collection of well defined objects is called SETS Examples • Set of Prime numbers • Set pupils of Tanglin Secondary School

Ways of representing a set • Roster Form : In this method all the members of the set are written within a pair of {} Set of natural numbers less than 7 can be written as { 1, 2, 3, 4, 5, 6}

Ways of representing a set • Set Builder : In this method a general element of the set is written within a pair of {} including the common property followed by all the elements Ex. Set of natural numbers less than 7 can be written as { x: x <7 ; x N}

Types of Sets 1. Finite set: A set with countable number of elements is known as finite set • EX. Set of pupils in Sec 3 of TSS 2 Infinite set: A set with uncountable number of elements is known as infinite set

Different Types of Sets 1. Null Set: A set with no elements is known as Null set or Empty Set Ex : Set of pupils who is 10 feet tall 2 Singleton Set: A set with only one element is known as Singleton set Ex: Set of prime numbers which is even

Different Types of Sets 3 4 Universal Set: A set which consists of all elements under consideration is known as Universal Set and it is denoted as Complement of a set A: It is a set of all elements of universal set but not the elements of A and it is denoted as A A = { x: x and x A } Ex. Let = { 1, 2, 3, 4, 5, 6, 7, 8, 9} and A= {1, 4, 5, 6} Then A = { 2, 3, 7, 8, 9}

Sub sets • A set A is a subset of another set B if every element of A is a member of B and represented as A B Illustration : Let A = {1, 3, 6, 8} B= { 1, 2, 3, 6, 7, 8} Then A B

Operations of Sets • Union: Union of two sets A and B is a set which consists of all the elements of A and B • In set notation A B = { x: x A or x B} Ex: Let A= {1, 3, 4, 6, 8, 9} & B= { 1, 2, 3, 6, 7, 8} Then A B = { 1, 2, 3, 4, 6, 7, 8, 9}

Operations of Sets • Intersection: Intersection of two sets A and B is a set which consists of the elements common to both A and B • In set notation A B = { x: x A & x B} Ex: Let A= {1, 3, 4, 6, 8, 9} & B= { 1, 2, 3, 6, 7, 8} Then A B = {1, 3, 6, 8}