Research on Judging a Transitive Bbinary-Relation

It is difficult to judge a transitive binary-relation by using the definition of transitivity of binary relation directly.Two equivalent definitions of transitivity are given in this paper.And several methods such as graph,matrix,compound of two binary-relations,transitive closure,etc.are used to identify the transitivity of binary-relation.The advantages and disadvantages of each method are discussed in detail,which is very helpful for the students to know well how to judge a transitive binary-relation.