Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is

Question

Philoid · Accepted Answer

This is because relation R is reflexive as (1, 1), (2, 2), (3, 3) ϵ R.

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

But relation R is not transitive as (3, 1), (1, 2) ϵ R but (3, 2) R.

Now, if we add any one of the two pairs (3, 2) and (2, 3) (or both) to relation R,

Then, relation R will become transitive.

Therefore, the total number of desired relations is one.