# Let be a relation on the set  The relation is Option 1) reflexive and symmetric only Option 2) an equivalence relation Option 3) reflexive only Option 4) reflexive and transitive only.

As we learnt in

Equivalence Relation -

A relation which is reflexive, symmetric & transitive is called Equivalence Relation.

-

Let R = {(3, 3) (6, 6) (9, 9) (12, 12) (6, 12) (3, 9) (3, 12) (3, 6)}

A = {3, 6, 9, 12}

Now,   but  so it is not symmetric.

Now

So  so it is transitive.

Correct option is 4.

Option 1)

reflexive and symmetric only

This is an incorrect option.

Option 2)

an equivalence relation

This is an incorrect option.

Option 3)

reflexive only

This is an incorrect option.

Option 4)

reflexive and transitive only.

This is the correct option.

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