# Mark the tick against the correct answer in the following:Let A = {1, 2, 3} and let R = {(1, 1),(2, 2), (3, 3), (1, 3), (3, 2), (1, 2)}. 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 = {1, 2, 3}

And R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2), (1, 2)}

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 , (1,1) R , (2,2) R , (3,3) R

Therefore , R is reflexive ……. (1)

Check for symmetric

Since (1,3) R but (3,1) R

Therefore , R is not symmetric ……. (2)

Check for transitive

Here , (1,3) R and (3,2) R and (1,2) R

Therefore , R is transitive ……. (3)

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

Correct option will be (B)

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