Types of Set

Types of Sets

In sets theory, there are many types of sets. Some of them are discussed below.

Singleton set

A set contains only one element.

For example, A = {3} and B = {star}. Here A and B are containing only one element so both are singleton sets.

Empty Set/Null Set

An empty set is a set with no element. It is denoted by A = { } or A = φ.

Finite Set

A set contains finite number of elements.

For example: A = { 2, 4, 6, 8, 10} and B = { a, v, q}. There are 5 objects in set A and 3 elements contained by set B.

Infinite set

If the number of elements in a set is infinite, the set is called an infinite set.

 For example, W= set of whole numbers = { 0, 1, 2, 3, 4, 5, ……}

Universal Set

Any set which is a superset of all the sets under consideration and usually it is denoted as S or U.

For example, Let P = {3, 4, 5} and Q = {1, 2, 3} then we take S = {1, 2, 3, 4, 5} as universe set.

Equal Sets

Two sets P and Q are equal if both are a subset of each other.

Mathematically: If P ⊆ Q and Q ⊆ P then P = Q.

For example, P = {3, 6, 8} and Q = {6, 3, 8}

Here P and Q have exactly the same elements. Satisfy the condition P ⊆ Q and Q ⊆ P.

Equivalent set

If the number of elements is the same for two different sets, then they are called equivalent sets. The order of sets does not matter here. It is represented as:

 n(A) = n(B)

where A and B are two different sets with the same number of elements.

Example: If A = {1,2,3,4} and B = {Red, Blue, Green, Pink}

In set A, there are four elements and in set B also there are four elements. Therefore, set A and set B are equivalent.

Disjoint Sets 

The two sets A and B are said to be disjoint if the set does not contain any common element.

Example: Set A = {1,2,3,4} and set B = {5,6,7,8} are disjoint sets, because there is no common element between them.