Let $A = \{1, 2, 3\}$. The number of equivalence relations containing (1, 3) is
Answer & explanation
Correct answer: option 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: $2$