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Singleton Set

Singleton set is a set containing only one element. The singleton set is of the form A = {a}, and it is also called a unit set. The singleton set has two subsets, which is the null set, and the set itself.

Let us learn more about the properties of singleton set, with examples, FAQs.

1. What Is A Singleton Set?
2. Properties Of Singleton Set
3. Examples On Singleton Set
4. Practice Questions
5. FAQs On Singleton Set

What Is A Singleton Set?

A singleton set is a set containing only one element. The singleton set is of the form A = {a}, Where A represents the set, and the small alphabet 'a' represents the element of the singleton set. Since a singleton set has only one element in it, it is also called a unit set. The cardinal number of a singleton set is one. The number of subsets of a singleton set is two, which is the empty set and the set itself with the single element.

The number of singleton sets that are subsets of a given set is equal to the number of elements in the given set. The set A = {a, e, i , o, u}, has 5 elements. Hence the set has five singleton sets, {a}, {e}, {i}, {o}, {u}, which are the subsets of the given set.

Properties Of Singleton Set

The following are some of the important properties of a singleton set.

  • The singleton set has only one element in it.
  • The cardinality of a singleton set is one.
  • The singleton set has two subsets.
  • Null set is a subset of every singleton set.
  • The two subsets of a singleton set are the null set, and the singleton set itself.
  • The powerset of a singleton set has a cardinal number of 2

Related Topics

The following topics help in a better understanding of singleton set.

 

Examples on Singleton Set

  1. Example 1: Find the subsets of the set A = {1, 3, 5, 7, 11} which are singleton sets.

    Solution:

    The given set is A = {1, 3, 5, 7, 11}.

    The given set has 5 elements and it has 5 subsets which can have only one element and are singleton sets.

    Therefore the five singleton sets which are subsets of the given set A is {1}, {3}, {5}, {7}, {11}.

  2. Example 2: Find the powerset of the singleton set {5}.

    Solution:

    The given singleton set is A = {5}.

    The two possible subsets of this singleton set are { }, {5}.

    The power set can be formed by taking these subsets as it elements.

    Powerset of A = {{ }, {5}}.

    Therefore the powerset of the singleton set A is {{ }, {5}}.

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FAQs on Singleton Set

What Is Singleton Set?

A set containing only one element is called a singleton set. The singleton set is of the form A = {a}. Since a singleton set has only one element in it, it is also called a unit set. The number of subsets of a singleton set is two, which is the empty set and the set itself with the single element.

What Is The Cardinal Number Of A Singleton Set?

The cardinal number of a singleton set is 1. The singleton set has only one element in it.

What Is The Other Name Of Singleton Set?

The singleton set has only one element, and hence a singleton set is also called a unit set.

What Are The Subsets Of Singleton Set?

The singleton set has two sets, which is the null set and the set itself. For a set A = {a}, the two subsets are { }, and {a}.

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