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In mathematics, the intersection ''A'' ∩ ''B'' of two sets ''A'' and ''B'' is the set that contains all elements of ''A'' that also belong to ''B'' (or equivalently, all elements of ''B'' that also belong to ''A''), but no other elements. For explanation of the symbols used in this article, refer to the table of mathematical symbols. ==Basic definition== The intersection of ''A'' and ''B'' is written "''A'' ∩ ''B''". Formally: : that is : ''x'' ∈ ''A'' ∩ ''B'' if and only if : * ''x'' ∈ ''A'' and : * ''x'' ∈ ''B''. For example: : * The intersection of the sets and is . : * The number 9 is ''not'' in the intersection of the set of prime numbers and the set of odd numbers .〔(How to find the intersection of sets )〕 More generally, one can take the intersection of several sets at once. The ''intersection'' of ''A'', ''B'', ''C'', and ''D'', for example, is ''A'' ∩ ''B'' ∩ ''C'' ∩ ''D'' = ''A'' ∩ (''B'' ∩ (''C'' ∩ ''D'')). Intersection is an associative operation; thus, ''A'' ∩ (''B'' ∩ ''C'') = (''A'' ∩ ''B'') ∩ ''C''. Inside a universe ''U'' one may define the complement ''A''c of ''A'' to be the set of all elements of ''U'' not in ''A''. Now the intersection of ''A'' and ''B'' may be written as the complement of the union of their complements, derived easily from De Morgan's laws: ''A'' ∩ ''B'' = (''A''c ∪ ''B''c)c 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「Intersection (set theory)」の詳細全文を読む スポンサード リンク
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