Question

(
a. Let the relation R be R = {(2, 1) (3, 2) (3,3)} on
& the transitive
the set of
set A = {1,2,3} .
what is the
transitive closure of R
​

Answer 1

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.

I hope it will help you