Subset

Subset

In mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.

Comment
enIn mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.
Depiction
Example of A is a proper subset of B.svg
Example of C is no proper subset of B.svg
PolygonsSet EN.svg
Subset with expansion.svg
Venn A subset B.svg
Has abstract
enIn mathematics, set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements. The subset relation defines a partial order on sets. In fact, the subsets of a given set form a Boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the Boolean inclusion relation.
Hypernym
Subset
Id
enSubset
Is primary topic of
Subset
Label
enSubset
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Binary relation
Binomial coefficients
Boolean algebra (structure)
Cardinality
Cardinal number
Cartesian product
Category:Basic concepts in set theory
Convex subset
Element (mathematics)
Empty set
Equal (math)
Euler diagram
File:PolygonsSet EN.svg
File:Subset with expansion.svg
File:Venn A subset B.svg
Hierarchy
If and only if
Inclusion (Boolean algebra)
Inclusion order
Ine (mathematics)
Inequality (mathematics)
Intersection (set theory)
Isomorphic
Join and meet
Line segment
Mathematics
Natural number
Order isomorphism
Ordinal number
Partial order
Powerset
Power set
Prime number
Rational number
Real number
Region (mathematics)
Set (mathematics)
Set membership
Set theory
Subset sum problem
There exists
Total subset
Transfinite number
Union (set theory)
Universal generalization
SameAs
4184620-5
Alamhulk
Alt küme
Azpimultzo
Binkom
Deelverzameling
Delmængde
Delmängd
Delmengd
Delmengde
Himpunan bagian
Hlutmengi
Inclusion
Inclusion (mathématiques)
Inclusione
irwk
Is-set
m.06wdz
Osajoukko
Podmnožica
Podmnožina
Podmnožina
Podskup
Podskup
Podzbiór
Q177646
Részhalmaz
Subaro
Subconjunt
Subconjunto
Subconjunto
Subinsimul
Submulțime
Subpangkat
Subset
Subset
Suttanzemi
Tập hợp con
Teilmenge
Υποσύνολο
Аййыш
Дэд олонлог
Падмноства
Подмножество
Подмножество
Подмножество
Подскуп
Підмножина
Ենթաբազմություն
תת-קבוצה
زیرمجموعه
مجموعة جزئية
ژێرکۆمەڵ
उपसमुच्चय
উপসেট
உட்கணம்
เซตย่อย
ታህታይ ስብስብ
子集
部分集合
부분집합
Subject
Category:Basic concepts in set theory
Thumbnail
Venn A subset B.svg?width=300
Title
enSubset
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Wikipage page ID
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Wikipage revision ID
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