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
The given set is A = {1, 2, 3}.
The smallest relation containing (1, 2) and (1, 3) which is reflexive and symmetric, but not transitive is given by:
R = {(1, 1), (2, 2), (3, 3), (1, 2), (1, 3), (2, 1), (3, 1)}
This is because relation $R$ is reflexive as $(1,1),(2,2),(3,3) \in R$.
Relation $R$ is symmetric since $(1,2),(2,1) \in R$ and $(1,3),(3,1) \in R$.
But relation $\mathrm{R}$ is not transitive as $(3,1),(1,2) \in \mathrm{R}$, but $(3,2) \notin \mathrm{R}$.
Now, if we add any two pairs (3, 2) and (2, 3) (or both) to relation R, then relation R will become transitive.
Hence, the total number of desired relations is one.
The correct answer is A.