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The relation "is the birth parent of" on a set of people is not a transitive relation. However, in biology the need often arises to consider birth parenthood over an arbitrary number of generations: the relation "is a birth ancestor of" ''is'' a transitive relation and it is the transitive closure of the relation "is the birth parent of".

The relation "is the birth parent of" on a set of people is not a transitive relation. However, in biology the need often arises to consider birth parenthood over an arbitrary number of generations: the relation "is a birth ancestor of" ''is'' a transitive relation and it is the transitive closure of the relation "is the birth parent of".

在一群人中的关系“XX是XX的亲生父母”不是一个传递关系。但是，生物学上，经常需要考虑任意多代人的亲生关系：关系“XX是XX的鼻祖”是一个传递关系，并且它是关系“XX是XX的亲生父母”的传递闭包。

在一群人中的关系“XX是XX的亲生父母”不是一个传递关系。但是，生物学上，经常需要考虑任意多代人的亲生关系：关系“XX是XX的鼻祖”是一个传递关系，并且它是关系“XX是XX的亲生父母”的传递闭包。

== Relation properties that require transitivity ==<br>

== Relation properties that require transitivity ==<br>

==依赖传递性的关系性质==

==依赖传递性的关系性质==