MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions
Problem
Let L be the set of all straight lines in a plane. A binary relation R on L is defined by lRm if and only if line l is parallel to line m.
(i) Define the terms reflexive relation, symmetric relation and transitive relation on a non-empty set.
(ii) For the above relation R, verify separately whether it is reflexive, symmetric and transitive. Give explicit reasons for every property you test.
(iii) State, with justification, whether R is an equivalence relation on L.