Set

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

Subsets

If every member of the set A is also a member of the set B, then A is said to be a subset of B, written A subseteq B, also pronounced A is contained in B. Equivalently, we can write B supseteq A, read as B is a superset of A, B includes A, or B contains A. The relationship between sets established by subseteq is called inclusion or containment.

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If A is a subset of but not equal to B, then A is called a proper subset of B, written A subset B (A is a proper subset of B) or B supset A (B is proper superset of A). However, in some literature these symbols are read the same as subseteq and supseteq, so it's often preferred to use the more explicit symbols subsetneq and supsetneq for proper subsets and supersets.

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A is a subset of B

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Examples:

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:*The set of all men is a proper subset of the set of all people.

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:*{1,3} subset {1,2,3,4}

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:*{1, 2, 3, 4} subseteq {1,2,3,4}

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The empty set is a subset of every set and every set is a subset of itself:

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:*emptyset subseteq A

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:*A subseteq A

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For more information about subsets, see Subset.

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