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

$R= \{(x, y): 3x-y=0\}$

$⇒y=3x$

Check Reflexivity,

$(x,x)∈R$

$⇒3x-x=0⇒2x=0$

which is only true for $x=0$, but $0∉A$

Check Symmetry,

$(1,3)∈R⇒3=3(1)$

But,

$(3,1)∉R$

∴ Not symmetric

Check transitivity,

$(x,y)∈R$ and $(y,z)∈R$

$⇒3x=y$ and $3y=z$

But, $(x,z)∉R$

∴ Not transitivity