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
Answer & explanation
Correct answer: option 1
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.