Let set $X = \{1, 2, 3\}$ and a relation $R$ is defined in $X$ as: $R = \{(1, 3), (2, 2), (3, 2)\}$. Then, the minimum ordered pairs that should be added in relation $R$ to make it reflexive and symmetric are:

$\{(1, 1), (3, 3), (3, 1), (2, 3)\}$

The correct answer is Option (3) → $\{(1, 1), (3, 3), (3, 1), (2, 3)\}$ ##

(i) $R$ is reflexive if it contains $\{(1, 1), (2, 2), \text{ and } (3, 3)\}$.

Since $(2, 2) \in R$ we need to add $(1, 1)$ and $(3, 3)$ to make $R$ reflexive.

(ii) $R$ is symmetric if it contains $\{(2, 2), (1, 3), (3, 1), (3, 2), (2, 3)\}$.

Since $\{(2, 2), (1, 3), (3, 2)\} \in R$, we need to add $(3, 1)$ and $(2, 3)$.

Thus, minimum ordered pairs which should be added in relation $R$ to make it reflexive and symmetric are $\{(1, 1), (3, 3), (3, 1), (2, 3)\}$.