# Mark the tick against the correct answer in the following:Let A = {a, b, c} and let R = {(a, a), (a, b), (b, a)}. Then, R isA. reflexive and symmetric but not transitiveB. reflexive and transitive but not symmetricC. symmetric and transitive but not reflexiveD. an equivalence relation

Given set A = {a, b, c}

And R = {(a, a), (a, b), (b, a)}

Formula

For a relation R in set A

Reflexive

The relation is reflexive if (a , a) R for every a A

Symmetric

The relation is Symmetric if (a , b) R , then (b , a) R

Transitive

Relation is Transitive if (a , b) R & (b , c) R , then (a , c) R

Equivalence

If the relation is reflexive , symmetric and transitive , it is an equivalence relation.

Check for reflexive

Since , (b,b) R and (c,c) R

Therefore , R is not reflexive ……. (1)

Check for symmetric

Since , (a,b) R and (b,a) R

Therefore , R is symmetric ……. (2)

Check for transitive

Here , (a,b) R and (b,a) R and (a,a) R

Therefore , R is transitive ……. (3)

Now , according to the equations (1) , (2) , (3)

Correct option will be (C)

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