Download Sets - GEOCITIES.ws

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 Sec3 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}