(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 = {(l_1, l_2) : l_1 is parallel to l_2}. 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 = 3x + 2, then find the set of rail lines in R related to it. OR (b) Let S be the relation defined by S = {(l_1, l_2) : l_1 is perpendicular to l_2} check whether the relation S is symmetric and transitive.