The relation R in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (1, 3), (2, 3)\}$ is:

both reflexive and transitive

The correct answer is Option (4) → both reflexive and transitive

Given set: $A = \{1, 2, 3\}$

Relation: $R = \{(1,1), (2,2), (3,3), (1,2), (1,3), (2,3)\}$

Check properties:

Reflexive: A relation is reflexive if $(a, a) \in R$ for all $a \in A$.

Here, $(1,1)$, $(2,2)$, $(3,3)$ are all in $R$ ⟹ Reflexive: Yes

Symmetric: If $(a, b) \in R$ then $(b, a) \in R$ must also be true.

$(1,2) \in R$ but $(2,1) \notin R$ ⟹ Symmetric: No

Transitive: If $(a,b) \in R$ and $(b,c) \in R$ then $(a,c) \in R$ must hold.

$(1,2), (2,3) \in R$ ⟹ check if $(1,3) \in R$ → Yes

No other such chain fails, so Transitive: Yes