Subset

In mathematics, especially in set theory, a set A is a subset of a set B, if A is "contained" inside B. The relationship of one set being a subset of another is called inclusion.

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More formally, If A and B are sets and every element of A is also an element of B, then:

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• A is a subset of (or is included in) B, denoted by A ⊆ B,

or equivalently

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• B is a superset of (or includes) A, denoted by B ⊇ A.

Every set B is a subset of itself.

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A subset of B which is not equal to B is called proper (or strict).

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If A is a proper subset of B, then one writes A ⊂ B.

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Analogous comments apply to supersets. For any set S, inclusion is a relation on the set of all subsets of S (the power set of S).

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Subset: Notational variations ►



 

Set theory: Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, of collections of objects, and the elements of, and membership in, such collections. It is the language in which mathematical objects a...

Set: :This article is about sets in mathematics. For other senses, see set (disambiguation)....

Element: The term element may mean:...