Q. $x_{2} = xy$ is a relation which is
A) Symmetric
B) Reflexive and transitive
C) Transitive
D) None of these
Explanation
(b)
Reflexive $xRx$
Since, $x^{2} = x.x$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ x^{2} = xy$
Transitive, $xRy \Rightarrow x^{2} = xy$
And $yRz \Rightarrow y^{2} = yz$
Now, $x^{2}y^{2} = xy^{2}z \Rightarrow x^{2} = xz$
$\Rightarrow xRz$
$\therefore$ It is transitive.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.