(4)

Given,

Set A = {1,2,3}

Now Cartesian product A x A = {(1,1), (2, 1), (1, 2), ........, (3,3)}

Now, given the relation is reflexive,

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

Also given (1, 2), (2, 3) R, (1,3) must R

Now finding, Possible cases:

Case-l: All of (2, 1), (3, 2), (3, 1) R 1 relation.

Case-2: Only one of (2, 1), (3, 2), (3, l) R 3 relations.

For example if relation is {(1, 1), (2, 2), (3, 3),(2,1)} then it is reflexive as well as transitive as (2, 2),(2,1) (2,1) is present in relation

Note that exactly two of (2, 1), (3, 2), (3,1) R is not possible because if two of these R, third must R to make relation transitive.

Total number of relations = 4

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