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In mathematics, the symmetric closure of a binary relation ''R'' on a set ''X'' is the smallest symmetric relation on ''X'' that contains ''R''. For example, if ''X'' is a set of airports and ''xRy'' means "there is a direct flight from airport ''x'' to airport ''y''", then the symmetric closure of ''R'' is the relation "there is a direct flight either from ''x'' to ''y'' or from ''y'' to ''x''". Or, if ''X'' is the set of humans (alive or dead) and ''R'' is the relation 'parent of', then the symmetric closure of ''R'' is the relation "''x'' is a parent or a child of ''y''". == Definition == The symmetric closure ''S'' of a relation ''R'' on a set ''X'' is given by : In other words, the symmetric closure of ''R'' is the union of ''R'' with its inverse relation, ''R'' -1. 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「symmetric closure」の詳細全文を読む スポンサード リンク
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