Let G = (V, E) be a loop-free undirected graph. Define the relation R on E as follows: If e1, e2 ∈ E, then e1 R e2 if e1 = e2 or if e1 and e2 are edges of a cycle C in G.
(a) Verify that R is an equivalence relation on E.
(b) Describe the partition of E induced by R.