帮忙翻译以下内容：
题目：二元关系具备传递性的充要条件的一种新的证明
关键词：二元关系，传递性，传递闭包
摘要：从传递闭包的角度证明了判定一个关系是否具备传递性的充要条件，给出并证明了一条关于关系合成运算的定理。
參考答案:楼上那位好象是用机器翻译的,挺搞笑的.
以下是老叮当的译文:
Title：A new proof of the sufficient and necessary condition for the Transitivity of the binary relations
Keyword：Binary relation，Transitivity，Transitive closure
Abstract： Sufficient and necessary condition for deciding whether a relation has Transitivity is proved from the point view of Transitive closure，a theorem about relation composition operation is also given and proved.