Research on Judging a Transitive Bbinary-Relation
Zhao Ming-ru
Abstract
Zhao Ming-ru
Abstract
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.
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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.
Key concepts: Transitive relation, Transitive closure, Binary relation, Transitive reduction, Relation (database), Mathematics, Logical matrix, Binary number