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.

Related Topics:
Mathematics - Set theory - Set

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

Related Topics:
Set - Element

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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).

Related Topics:
Relation - Power set

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Subset: Notational variations ►