Let a relation R in the set N of natural numbers be defined as $(x, y) ∈ R$ iff $x^2-4xy+ 3y^2 =0$ for all $x, y ∈ N$. The relation R is

reflexive and transitive

The correct answer is Option (1) → reflexive and transitive

It is given that

$(x, y) ∈ R ⇔ x^2-4xy + 3y^2 = 0$

$⇔(x-3y) (x-y)=0⇔x=y$ or $x=3y$

$∴R=\{(y, y): y ∈N\}∪\{(3y, y): y ∈N\}$

Clearly, R is reflexive and transitive but not symmetric.