Math, asked by abhishek2662, 11 months ago

conditions of transitive relation

Answers

Answered by MitanshuJain

"Transitive relation. In mathematics, a binary relation R over a set X istransitive if whenever an element a is related to an element b and b is related to an element c then a is also related to c. Transitivity (or transitiveness) is a key property of both partial orderrelations and equivalence relations."

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abhishek2662: I know this conditions but how can we solve problems

Answered by SidVK

A Relation ‘R' which is defined by a set ‘A' is called a Transitive Relation, if =>

(a1 , a2) € R

(a2 , a3) € R

And, (a1 , a3) € R.........where a1,a2,a3 € A.

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{€ means ‘belongs to'}

Hope it was helpful.

abhishek2662: I know this conditions but how can we solve problems

SidVK: For example=> xRy = { (1,2) , (1,3) , (1,4) , (1,7) , (2,3) , (2,5) , (3,9) , (1,9) }. In this relation set you can see that we have (1,3) , (3,9) , (1,9).....and it satisfies the condition of a transitive relation. Thus, it is. a transitive relation. This is the wat to solve

abhishek2662: A={1,2,3} define a reln. on A such that R is reflexive, symmetric and transitive. R={(1,1),(2,2),(3,3)} then can u tell me how it is transitive?

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