Question

check the relation R={(1,1),(2,2),(3,3),.......,(n,n)} defined on the set S ={1,2,3, 4,...n} for the three basic relations.

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Answer 1

Answer:

Therefore, its an equivalence relation.

Explanation:

Given Relation

R={(1,1),(2,2),(3,3),.........................(n,n)}

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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