Transitive Relation

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A Transitive Relation is a Binary Relation where two elements are related if they are already related by an intermediary element.



    • Definition(transitive relation): A relation [math]\displaystyle{ R }[/math] on a set A is called transitive if and only if for any a, b, and c in A, whenever [math]\displaystyle{ R }[/math] <a, b> R, and <b, c> R, <a, c> [math]\displaystyle{ R }[/math] .
    • Example 8: The relation on the set of integers {1, 2, 3} is transitive, because for <1, 2> and <2, 3> in, <1, 3> is also in, for <1, 1> and <1, 2> in, <1, 2> is also in, and similarly for the others. As a matter of fact on any set of numbers is also transitive. Similarly and = on any set of numbers are transitive.