Finite set-

If the number of elements of a set is finite, the set is called a finite set

Example – a)  { The set of all the month of the year }

            b)  X = { x : x is a factor of 6 }

            c)  The set of even numbers between 5 to 25


Infinite Set –

If in a set there are don’t have any fixed number of elements is called an infinite set, such a set has an uncountable number of elements.


 a) The of all positive even integers   

 b) The set of integers I = { ………, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,………….. }

 c) The set of natural numbers that are greater than 9 = { x : x N and  x > 9 }


Empty Set –

If any A set that does not contain any elements is to be considered as an Empty set, such a set is donated by { } or φ. An empty set is also called Null Set or a Vold set,

Example –

 a) the set of women who are 6 meters tall

 b) the set of odd integers with 6 as a factor

 c) the set of even prime numbers that are greater than 7

the number of elements in an empty set is 0, but { 0 } is not an empty set because it contains the elements 0.

Universal Set –

The set of all the possible objects (or elements), under consideration for a particular discussion, is called the Universal set and it is denoted by U, the universal set may be different for different problems.


          Let, A = { students of your class who play cricket }

                B = { students of your class who play football }

If our study is regarding the sets A & B, we may take the set of all the students of your class as the universal set, we may also take the set of all the students of your school as the universal set, however in a particular problem there will be only one universal set.

Equivalent set –

This is to be remembered that, two finite set would be called Equivalent set, whether they contain the same number of elements, In other words, sets A & B are equivalent sets if n(A) = n(B), we express this in symbols as A ↔ B


The sets A = { 2, 5, 8, 12 }, and  B = { 4, 6, 9, 11 } are considered as equivalent sets because it has been observed that, n(A) = n(B) = 4, In symbol A ↔ B.

Singleton Set –

A set that has only one element is called a Singleton Set.

Example – Each of the sets { 0 }, { 2 }, { 5 } are Singleton set.