
In mathematics, especially in set theory, a set ''A'' is a subset of a set ''B'', or equivalently ''B'' is a superset of ''A'', if ''A'' is "contained" inside ''B'', that is, all elements of ''A'' are also elements of ''B''. ''A'' and ''B'' may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment. The subset relation defines a partial order on sets. The algebra of subsets forms a Boolean algebra in which the subset relation is called inclusion. ==Definitions== If ''A'' and ''B'' are sets and every element of ''A'' is also an element of ''B'', then: : * ''A'' is a subset of (or is included in) ''B'', denoted by $A\; \backslash subseteq\; B$, :or equivalently : * ''B'' is a superset of (or includes) ''A'', denoted by $B\; \backslash supseteq\; A.$ If ''A'' is a subset of ''B'', but ''A'' is not equal to ''B'' (i.e. there exists at least one element of B which is not an element of ''A''), then : * ''A'' is also a proper (or strict) subset of ''B''; this is written as $A\backslash subsetneq\; B.$ :or equivalently : * ''B'' is a proper superset of ''A''; this is written as $B\backslash supsetneq\; A.$ For any set ''S'', the inclusion relation ⊆ is a partial order on the set $\backslash mathcal(S)$ of all subsets of ''S'' (the power set of ''S''). When quantified, is represented as: }. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「subset」の詳細全文を読む スポンサード リンク
