Question

check the relation R = {(1, 1) }, (2, 2), (3, 3),...(n, n) } defined on the sets s= {1, 2,3,.....n} for the three basic relation

plz give very crt answer I want urgently plz help me​

Answer 1

Answer:

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.