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.
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}.
