Let $A = \{1, 2, 3\}$. The number of equivalence relations containing (1, 3) is

2

The correct answer is Option (2) → 2

Set $A = \{1,2,3\}$

An equivalence relation partitions $A$ into disjoint subsets (equivalence classes). Given that $(1,3)$ is in the relation, 1 and 3 must belong to the same equivalence class.

Possible partitions containing 1 and 3 together:

1) $\{1,3\}, \{2\}$ → 1 equivalence relation

2) $\{1,2,3\}$ → 1 equivalence relation

Total: $2$ equivalence relations

Answer: $2$