Superset vs. Subset: What's the Difference?
Edited by Aimie Carlson || By Harlon Moss || 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.
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.
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.
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.
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.
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Comparison Chart
Definition
A set containing all elements of another set
A set whose elements are all contained in another set
Size
Generally larger or equal to the subset
Smaller or equal to the superset
Inclusion
Includes all elements of the subset, possibly more
Only includes elements that are in the superset
Relationship
Encompasses the subset
Is encompassed by the superset
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
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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.
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.
Superset
A set that includes another set entirely.
The set of all vehicles is a superset of the set of all cars.
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.
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.
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.
Superset
A set encompassing every element of its subset.
For the set of all books, the library's collection is a superset.
Subset
A set entirely included within another set.
The set of all mystery novels is a subset of the set of all novels.
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.
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.
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".
Subset
A set contained within a set.
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.
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 is a both a subset and a proper subset of while the set is a subset of but not a proper subset of .
Superset
To perform (different physical exercises) back to back, without a period of rest between them.
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.
Subset
(transitive) To take a subset of.
Subset
To extract only the portions of (a font) that are needed to display a particular document.
Subset
A set whose members are members of another set; a set contained within another set
FAQs
Can a set be both a superset and a subset?
Yes, every set is a subset and a superset of itself.
Does a superset always have more elements than its subset?
Not necessarily; a set can be a superset of itself without having more elements.
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.
Can one set have multiple supersets?
Yes, a set can have many supersets that include it.
Are these terms only used in mathematics?
While common in mathematics, they are also used in other fields like computer science and data analysis.
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.
Is the empty set a subset of every set?
Yes, the empty set is considered a subset of every set.
Can a subset have elements not in the superset?
No, all elements of a subset must be in the superset.
Can subsets overlap?
Subsets of different sets can overlap if they share common elements.
Does changing an element in a set affect its subsets?
It can, especially if the changed element is part of the subsets.
Can a subset become a superset?
Yes, in relation to its own subsets, a subset can be a superset.
Do subsets have to be contiguous?
No, the elements of a subset do not need to be contiguous.
Is a singleton set a subset?
Yes, a singleton set is a subset of any set containing that single element.
Can a subset be empty?
Yes, the empty set is a subset of every set.
Is there a limit to the size of a superset?
No theoretical limit, but practical limits exist based on the context.
How are subsets and supersets used in data analysis?
They are used to categorize and analyze different groupings of data points.
Are the terms 'subset' and 'subgroup' synonymous?
In general usage, they are similar, but 'subgroup' has specific meanings in fields like algebra.
How many subsets can a set have?
A set with 'n' elements has 2^n subsets, including the empty set and the set itself.
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.
Can these concepts apply to infinite sets?
Yes, they apply to both finite and infinite sets.
About Author
Written by
Harlon MossHarlon is a seasoned quality moderator and accomplished content writer for Difference Wiki. An alumnus of the prestigious University of California, he earned his degree in Computer Science. Leveraging his academic background, Harlon brings a meticulous and informed perspective to his work, ensuring content accuracy and excellence.
Edited by
Aimie CarlsonAimie Carlson, holding a master's degree in English literature, is a fervent English language enthusiast. She lends her writing talents to Difference Wiki, a prominent website that specializes in comparisons, offering readers insightful analyses that both captivate and inform.
