# Superset vs. Subset: What's the Difference?

Edited by Huma Saeed || By Sumera Saeed || Updated on November 13, 2023
A superset is a set that includes all the elements of another set, while a subset is a set whose elements are all contained within another set.

## Key Differences

A superset is a larger set that contains all elements of a smaller set within it. Conversely, a subset is that smaller set whose all elements are included in the superset.
Sumera Saeed
Nov 13, 2023
In mathematical terms, if set A is a subset of set B, then set B is a superset of set A, meaning all elements of A are also in B. However, B may contain additional elements not in A.
Sumera Saeed
Nov 13, 2023
The concept of subset implies a set being fully contained within another without any additional elements. In contrast, a superset encompasses the subset and possibly more elements.
Huma Saeed
Nov 13, 2023
Every set is a subset of itself and also a superset of itself, demonstrating the relative nature of these terms. This principle shows the inclusivity of the set concept in mathematics.
Sumera Saeed
Nov 13, 2023
The terms are used not only in mathematics but also in broader contexts, like data science, where subset and superset describe the relationship between data groups.
Aimie Carlson
Nov 13, 2023

## Comparison Chart

### Definition

A set containing all elements of another set
A set whose elements are all contained in another set
Sumera Saeed
Nov 13, 2023

### Size

Generally larger or equal to the subset
Smaller or equal to the superset
Sumera Saeed
Nov 13, 2023

### Inclusion

Includes all elements of the subset, possibly more
Only includes elements that are in the superset
Sumera Saeed
Nov 13, 2023

### Relationship

Encompasses the subset
Is encompassed by the superset
Aimie Carlson
Nov 13, 2023

### Example

If A = {1, 2}, then B = {1, 2, 3} is a superset of A
If B = {1, 2, 3}, then A = {1, 2} is a subset of B
Aimie Carlson
Nov 13, 2023

## Superset and Subset Definitions

#### Superset

A larger set in a set-subset relationship.
In a collection of fruits, the set of all fruits is a superset of the set of all apples.
Janet White
Nov 13, 2023

#### Subset

A smaller or equal set in a set-subset relationship.
The set of red apples is a subset of the set of all apples.
Harlon Moss
Nov 13, 2023

#### Superset

A set that includes another set entirely.
The set of all vehicles is a superset of the set of all cars.
Huma Saeed
Nov 13, 2023

#### Subset

A set whose elements are all contained in another set.
The set of all squares is a subset of the set of all rectangles.
Janet White
Nov 13, 2023

#### Superset

A set that is equal to or larger than another set.
The set of natural numbers is a superset of the set of prime numbers.
Janet White
Nov 13, 2023

#### Subset

A set comprised of some or all elements of a larger set.
The set of vowels is a subset of the set of letters in the alphabet.
Janet White
Nov 13, 2023

#### Superset

A set encompassing every element of its subset.
For the set of all books, the library's collection is a superset.
Sumera Saeed
Nov 13, 2023

#### Subset

A set entirely included within another set.
The set of all mystery novels is a subset of the set of all novels.
Huma Saeed
Nov 13, 2023

#### Superset

A set that contains all elements of a specific subset.
The set of all animals is a superset of the set of all dogs.
Harlon Moss
Nov 13, 2023

#### Subset

A set that is part of a larger set.
The set of weekdays is a subset of the set of all days in a week.
Sumera Saeed
Nov 13, 2023

#### Superset

(set theory) (symbol: ⊇) With respect to another set, a set such that each of the elements of the other set is also an element of the set.
The set of human beings is a superset of the set of human children.
The set of characters "LBPG" is a superset of the set of characters "PG".
Sumera Saeed
Dec 13, 2022

#### Subset

A set contained within a set.
Sumera Saeed
Dec 13, 2022

#### Superset

(weightlifting) Two or more different physical exercises performed back to back, without a period of rest between them. The exercises may employ the same muscle group, or opposing muscle groups.
Sumera Saeed
Dec 13, 2022

#### Subset

A set A such that every element of A is also an element of S.
The set of integers is a subset of the set of real numbers.
The set $\lbrace a, b\rbrace$ is a both a subset and a proper subset of $\lbrace a, b, c\rbrace$ while the set $\lbrace a, b, c\rbrace$ is a subset of $\lbrace a, b, c\rbrace$ but not a proper subset of $\lbrace a, b, c\rbrace$.
Sumera Saeed
Dec 13, 2022

#### Superset

To perform (different physical exercises) back to back, without a period of rest between them.
Sumera Saeed
Dec 13, 2022

#### Subset

A group of things or people, all of which are in a specified larger group.
We asked a subset of the population of the town for their opinion.
Sumera Saeed
Dec 13, 2022

#### Subset

(transitive) To take a subset of.
Sumera Saeed
Dec 13, 2022

#### Subset

To extract only the portions of (a font) that are needed to display a particular document.
Sumera Saeed
Dec 13, 2022

#### Subset

A set whose members are members of another set; a set contained within another set
Sumera Saeed
Dec 13, 2022

## FAQs

#### Can a set be both a superset and a subset?

Yes, every set is a subset and a superset of itself.
Sumera Saeed
Nov 13, 2023

#### Does a superset always have more elements than its subset?

Not necessarily; a set can be a superset of itself without having more elements.
Huma Saeed
Nov 13, 2023

#### Is a subset always smaller than the superset?

A subset is usually smaller, but it can be equal to the superset when it is the set itself.
Aimie Carlson
Nov 13, 2023

#### Can one set have multiple supersets?

Yes, a set can have many supersets that include it.
Harlon Moss
Nov 13, 2023

#### Are these terms only used in mathematics?

While common in mathematics, they are also used in other fields like computer science and data analysis.
Sumera Saeed
Nov 13, 2023

#### How do you determine if a set is a subset of another?

A set is a subset of another if all its elements are contained in the other set.
Sumera Saeed
Nov 13, 2023

#### Is the empty set a subset of every set?

Yes, the empty set is considered a subset of every set.
Sumera Saeed
Nov 13, 2023

#### Can a subset have elements not in the superset?

No, all elements of a subset must be in the superset.
Harlon Moss
Nov 13, 2023

#### Can subsets overlap?

Subsets of different sets can overlap if they share common elements.
Janet White
Nov 13, 2023

#### Does changing an element in a set affect its subsets?

It can, especially if the changed element is part of the subsets.
Sumera Saeed
Nov 13, 2023

#### Can a subset become a superset?

Yes, in relation to its own subsets, a subset can be a superset.
Harlon Moss
Nov 13, 2023

#### Do subsets have to be contiguous?

No, the elements of a subset do not need to be contiguous.
Sumera Saeed
Nov 13, 2023

#### Is a singleton set a subset?

Yes, a singleton set is a subset of any set containing that single element.
Janet White
Nov 13, 2023

#### Can a subset be empty?

Yes, the empty set is a subset of every set.
Aimie Carlson
Nov 13, 2023

#### Is there a limit to the size of a superset?

No theoretical limit, but practical limits exist based on the context.
Aimie Carlson
Nov 13, 2023

#### How are subsets and supersets used in data analysis?

They are used to categorize and analyze different groupings of data points.
Harlon Moss
Nov 13, 2023

#### Are the terms 'subset' and 'subgroup' synonymous?

In general usage, they are similar, but 'subgroup' has specific meanings in fields like algebra.
Aimie Carlson
Nov 13, 2023

#### How many subsets can a set have?

A set with 'n' elements has 2^n subsets, including the empty set and the set itself.
Aimie Carlson
Nov 13, 2023

#### Are there real-life examples of these concepts?

Yes, like a pack of cards where hearts are a subset of all cards, and all cards are a superset of hearts.
Harlon Moss
Nov 13, 2023

#### Can these concepts apply to infinite sets?

Yes, they apply to both finite and infinite sets.
Sumera Saeed
Nov 13, 2023