If $A = \{1, 2, 3\}$ and consider the relation $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$. Then, $R$ is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → reflexive but not symmetric ##
Given that, $A = \{1, 2, 3\}$
and $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\}$
$∵(1, 1), (2, 2), (3, 3) \in R$
Hence, $R$ is reflexive.
$(1, 2) \in R \text{ but } (2, 1) \notin R$
Hence, $R$ is not symmetric.
$(1, 2) \in R \text{ and } (2, 3) \in R$
$\Rightarrow (1, 3) \in R$
Hence, $R$ is transitive.