Types of  Sets

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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.

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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
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