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