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.
a. (i) Define the terms reflexive relation, symmetric relation and transitive relation on a non-empty set.
b. (ii) For the above relation R, verify separately whether it is reflexive, symmetric and transitive. Give explicit reasons for every property you test.
c. (iii) State, with justification, whether R is an equivalence relation on L.