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单词 intersection
释义

intersection

The intersection of sets A and B is the set consisting of all elements that belong to both A and B, and it is denoted by A ∩ B (read as ‘A intersect B' or ‘A cap B'). The term ‘intersection' is used for both the resulting set and the operation, a binary operation on the set of all subsets of a set. The following properties hold:

(i) For all A, A ∩ A = A and A∩Ø=Ø.
(ii) For all A and B, A ∩ B = B∩A; that is, ∩ is commutative.
(iii) For all A, B and C, (A ∩ B)∩ C = A∩(B ∩ C); that is, ∩ is associative.

Given a family of sets Ai with index set I, then the intersection

consists of those elements x such that x is an element of Ai for all i in I. For the intersection of two events, see event.

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更新时间:2025/4/29 19:44:45