Question

If A={1,2,3}. Then find the number of reflexive relations in A​

Answer 1

Answer:

Solution :

Here, A={1,2,3}

R1={(1,1),(2,2),(3,3)(1,2)(1,3)(2,1)(3,1)(3,2)(2,3)}

We will work with the relations that contains (1,2),(3,1).

Relation R is reflexive as (1,1)(2,2)(3,3)∈R

Relation R is symmetric as (1,2),(2,1)∈R and (1,3)(3,1)∈R.

Relation R is not transitive since (3,1)(1,2)∈R but (3,2)∉R.

Therefore the total number of relation containing (1,2)(1,3) which are reflexive ,symmetric but not transitive is 1.

However if we add the pair (3,2) and (2,3) to relation R then it will become transitive. Therefore, the correct answer is 1 (A).

Hope it helps