## 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}

**☛See also:**

Special Mathematical Constants

SETS (Unit Test Paper)

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