Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3)

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.