# Types of Sets

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**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

• 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

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