(a) Students of a school are taken to a railway museum to learn about railways heritage and its history.

An exhibit in the museum depicted many rail lines on the track near the railway station. Let $L$ be the set of all rail lines on the railway track and $R$ be the relation on $L$ defined by

$R=\left\{l_1, l_2\right): l_1$ is parallel to $\left.l_2\right\}$

On the basis of the above information, answer the following questions:

(i) Find whether the relation R is symmetric or not.

(ii) Find whether the relation R is transitive or not.

(iii) If one of the rail lines on the railway track is represented by the equation $y=3 x+2$, then find the set of rail lines in R related to it.

OR

(b) Let $S$ be the relation defined by $S=\left\{\left(l_1, l_2\right): l_1\right.$ is perpendicular to $l_2$ \} check whether the relation $S$ is symmetric and transitive.