Let $$R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\}$$ be a relation on the set $$A = \{1, 2, 3, 4\}$$. The relation $$R$$ is

The relation R is neither reflexive, nor symmetric, nor transitive.

Given set and relation:

$$ A = \{1, 2, 3, 4\} $$

$$ R = \{(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)\} $$

Reflexivity check:

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

$$ (1, 1) \notin R $$

Therefore, R is not reflexive.

Symmetry check:

A relation is symmetric if $$ (a, b) \in R \implies (b, a) \in R $$.

$$ (2, 3) \in R $$

$$ (3, 2) \notin R $$

Therefore, R is not symmetric.

Transitivity check:

A relation is transitive if $$ (a, b) \in R \text{ and } (b, c) \in R \implies (a, c) \in R $$.

$$ (4, 2) \in R \text{ and } (2, 3) \in R $$

$$ (4, 3) \notin R $$

Therefore, R is not transitive.

Final Answer:

The relation R is not reflexive, not symmetric, and not transitive.From options it is Not Symmetric.