The number of equivalence relation on the set 1,2, 3 containing (1, 2…

The correct answer is Option (2) → 2

Given set $A = \{1, 2, 3\}$ and the relation contains $(1,2)$ and $(2,1)$.

For an equivalence relation, it must be reflexive, symmetric, and transitive.

Since $(1,2)$ and $(2,1)$ are in $R$, transitivity implies $(1,1)$ and $(2,2)$ must also be in $R$.

Hence, $1$ and $2$ belong to the same equivalence class $\{1,2\}$.

The third element $3$ may either:

• remain separate as $\{3\}$, giving partition $\{\{1,2\}, \{3\}\}$
• or join them, giving partition $\{\{1,2,3\}\}$

Thus, the number of such equivalence relations = 2.

Final Answer: 2