Question

The relation R in the set of natural number N is defined by $xRy\iff x^2-4xy+3y^2=0,$ $x,y\in N$ then R is

• A. reflexive but not symmetric and not transitive
• B. symmetric but not reflexive and not transitive
• C. transitive but not reflexive and not symmetric
• D. equivalence relation

Answer 1

The correct option is A reflexive but not symmetric and not transitive

$x^2-4xy+3y^2-0$
$x^2-3xy-xy+3y^2=0$
$x(x-3y)-y(x-3y)=0$
$(x-3y)(x-y)=0$
$x=3y,y$
$xRy=(x,y)x=y$ Reflexive
$xRy=(x,y):x=3y$
So it is reflexive but not symmetric and not transitive.