Let `R` be a relation on the set of all lines in a plane defined by `(l_1,\ l_2) in R ` <=> line `l_1` is parallel to line `l_2` . Show that `R` is an equivalence relation.

Explanation

`R={(L_{1}, L_{2}): L_{1}` is parallel to `L_{2}}`



`R` is reflexive as any line `L_{1}` is parallel to itself i.e., `(L_{1}, L_{1}) \in R`.



Now,



Let `(L_{1}, L_{2}) \in R`.



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