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r={(1,2),(1,1),(2,1),(2,2),(3,3),(1,3),(3,1),(2,3)} is an equivalence relation? How?

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r={(1,2),(1,1),(2,1),(2,2),(3,3),(1,3),(3,1),(2,3)} is an equivalence relation? How?

Posted by Kvs Manisha 3 years, 11 months ago

CBSE > Class 12 > Mathematics

2 answers

Sumit Pundeer 3 years, 11 months ago

There's no (3,2) how can be this symmetric?

Shruti Kumari 3 years, 11 months ago

Given Relation R={(1,1),(2,2),(3,3)} Reflexive: If a relation has {(a,b)} as its element, then it should also have {(a,a),(b,b)} as its elements too. Symmetric: If a relation has (a,b) as its element, then it should also have {(b,a)} as its element too. Transitive: If a relation has {(a,b),(b,c)} as its elements, then it should also have {(a,c)} as its element too. Now, the given relation satisfies all these three properties. Therefore, its an equivalence relation.

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