# Types of  Sets

Types of Sets are explained below :

1) Singleton sets: A set which contains only one element is known as Singleton set .

Examples :

1) If P = { x | x is a prime number 10 and 12 } then P = {11}

As we observe that there is only one element in set P.
n(P) = 1

so
set P is a singleton set.

2) If A = { x| x ∉ 3 < x < 5 } then

A = { x| x ∉ 3 < x < 5 }

A = { 4}

As the set A contains only one element so set A is a singleton set.

2) Finite sets : The sets in which number of elements are limited and can be counted, such sets are called finite sets.

Example :

If A= { x | x is a prime number, x<10 } then A= { 2,3,5,7}

Here then there are only 4 elements which satisfies the given condition.

Thus,
set A is a finite set.

3) Infinite sets : The sets in which number of elements are unlimited and can not be counted, such sets are called infinite sets .

Example :

set C = { 10,20,30,40,50,60,…}

As the number of elements in set C are infinity (uncountable)
Thus,
set C is an infinite set.

4) Empty set : A set which has no element in it and is denoted by φ
( Greek letter ‘phi’)

Thus n(φ) = 0

It is also known as
null set or void set .

Example :

set A ={ 18 < x < 19}

So between 18 and 19 there is no element.

Thus,
set A is an empty set.

Set Theory

Sets
Representation of Set
Cardinal Number
Types of Sets
Pairs of Sets
Subset
Complement of Set
Union of the Sets
Intersection of Sets
Operations on Sets
De Morgan's Law
Venn Diagrams
Venn-diagrams for sets
Venn-diagrams for different situations
Problems on Intersection of Two Sets
Problems on Intersection of Three Sets