A relation R on the set $A = \{1,2,3,........ 13, 14\}$ defined as $R = \{(x,y): 3x - y = 0\}$ is

Neither reflexive nor symmetric nor transitive

The correct answer is Option (4) → Neither reflexive nor symmetric nor transitive

$A=\{1,2,\ldots,14\},\;R=\{(x,y):3x-y=0\}\;\Rightarrow\;y=3x$

$\text{Pairs in }R:$ for $x\in A$ with $3x\in A\Rightarrow x\le 4$.

$R=\{(1,3),(2,6),(3,9),(4,12)\}$

$\text{Reflexive?}$ Needs $(a,a)$ for all $a\in A$; none of $(a,a)$ are in $R$ $\Rightarrow$ not reflexive.

$\text{Symmetric?}$ $(1,3)\in R$ but $(3,1)\notin R$ $\Rightarrow$ not symmetric.

$\text{Transitive?}$ $(1,3)\in R$ and $(3,9)\in R$ but $(1,9)\notin R$ $\Rightarrow$ not transitive.

Neither reflexive nor symmetric nor transitive