## Different Types of Sets

Class 11 - Mathematics

Empty Set:
A set is said to be empty set if it does not have any element. It is denoted by Φ or {}. Empty set is also called a null set or void set.
For example, The set of all odd natural numbers divisible by 2 is an empty set because odd natural numbers are not divisible by 2.

Finite Set:
A set which contains finite number of elements is called a finite set.
For example, The set {x: x ∈  N and x ≤ 10} is a ﬁnite set because number of elements in the set are countable.

Inﬁnite Set:
A set which is not ﬁnite or which contains inﬁnite number of elements is called an inﬁnite set.

For example, the set of points on a line is an inﬁnite set because a line have inﬁnite points on it.

Singleton Set:
A set which contains only one element is called singleton set.
For example: {9} is a singleton set.

Equal Sets:
Two sets are said to be equal sets if they have same elements.

For example: Let A : {2, 4, 6, 8} and B : {x : x is an even natural number less than 10) are two equal sets because we can write B in roster form as
B = {2, 4, 6, 8}

Hence, A = B.

Equivalent Sets:
The two sets A and B are said to be equivalent ifn(A) = n(B)
For example: A : {2, 3, 5} and B : {a, b, c}
n(A) : n(B) : 3

Universal Set:
A set which contain elements of all sets in a given context is called universal set. It is denoted by U.

e.g. if A = {1,2},  B = {1,2,3} and  C = {1,3,4}  then U = {1,2,3,4}  