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What are transitive relations?


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Solution

Define transitive relations.

Relation means two objects or quantities or elements of a set are related if there is a recognizable connection or link between the two objects or quantities or elements.

Example: If (a,b)R, we say that a is related to b under the relation R where aand bare objects or quantities or elements of a set

Transitive Relation:

A relation R in a setA is called transitive, if (x,y)R,(y,z)R then(x,z)R, for allx,yandzA.

For example: Let A=a,b,c,d and R be a relation on A in such way that

fora andb,a,bR:aandbarebrothers

also for bandc,b,cR:bandcarebrothers

then this relation R must exist for aand c a,cR:aandcarebrothers here the relation is transitive.

Hence, For a transitive relation in the setA ,If(x,y)R,(y,z)R, then(x,z)R where x,yandzA


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