(a) Students of a school are taken to a railway museum to learn about railways heritage and itg 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={(l₁,l₂) : l₁ is parallel to l₂}
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 ={(l₁,l₂) : l₁ is perpendicular to l₂ } check whether the relation S is symmetric and transitive.

Solution

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