Singleton set is a set with only one element. An example of a singleton set is an even prime number since there is only one prime number and all other primes are odd. Thus, the set of even prime numbers is a singleton set.

In this article, we will explore the singleton set, singleton set definition, singleton set symbol, singleton set examples, the cardinality of the singleton set, the power set of the singletons set, and others in detail.

What is Singleton Set?

A set is referred to as a singleton set when the number of elements in the set is one. The set of the form S = {a} is called a singleton set. The singleton sets are always finite as it has only 1 element.

Singleton Set Definition

Singleton set is defined as a set containing only one element. In other words, the set with one element is called a singleton set. The singleton set is also known as a unit set as the number of elements in the singleton set is a unit.

Singleton Set Symbol

The symbol of the singleton set is written as:

P = {x}

where:

• P is a singleton set with an element x

Singleton Set Examples

All the sets with only one element are singleton sets. Some examples of singleton sets are:

• Set of even prime numbers
• Set B = {10}
• Set Q = {|x|: x² = 16}

Cardinality of Singleton Set

The cardinality of singleton set is 1 as the number of elements present in the singleton set is 1. Since the singleton set contains only one element the cardinal number of singleton set is 1.

Cardinality of Singleton Set = 1

Power Set of a Singleton Set

The power set of a singleton set contains two elements the null set and the singleton set itself. The cardinality of the power set of a singleton set is 2 as it contains only two elements.

Properties of the Singleton Set

Some properties of singleton set are:

• Singleton set has only 1 element.
• Singleton set has the cardinality one.
• The singleton sets are always finite sets as the number of elements in the singleton set is 1.
• The number of subsets of singleton set is 2 i.e., empty set and the singleton set itself.
• The cardinality of power set of singleton set is 2.
• Empty set is subset of every singleton set.
• The union of two singleton set is singleton when the two sets are same.

Venn Diagram of a Singleton Set

Venn diagrams are the pictorial representations of any set. Below Venn diagram represents a singleton set.

Venn Diagram of a Singleton Set

Singleton Set Vs Empty Set

The table below gives us the difference between the singleton set and empty set.