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.