离散数学中关系交与复合的传递闭包  

The Transitive Closures of Intersection and Compound ofRelations in Discrete Mathematics

作　　者：谭尚旺 宁文杰 TAN Shang-wang;NING Wen-jie(School of Science, China University of Petroleum (East China), Qingdao Shandong 266580, China)

机构地区：[1]中国石油大学(华东)理学院,山东青岛266580

出　　处：《大学数学》2021年第5期94-98,共5页College Mathematics

摘　　要：借助关系图的概念,确定了有限集合上关系的传递闭包运算对交运算、复合运算和幂运算满足分配律的充分必要条件.特别是当关系是自反的或传递的时,证明关系的传递闭包运算对幂运算是满足分配律的.With some concepts of the relation graph,this paper determines sufficient and necessary conditions of the relations defined on a finite set whose transitive closure operation satisfies distributive laws to intersection operation,compound operation and power operation.In particular,we prove that transitive closure operation satisfies distributive laws to power operation when the relation is reflexive or transitive.

关 键 词：关系 复合运算 传递闭包 有向通路 

分 类 号：O144.5[理学—数学]