Q. 164.4( 8 Votes )

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

B. 2

C. 3

D. 4

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.

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