Infinite paths. Let G=(V,E) be a directed graph with a designated "start vertex" sV, a set VGV of "good" vertices, and a set VBV of "bad" vertices. An infinite trace p of G is an infinite sequence v0v1v2 of vertices viV such that (1) v0=s, and (2) for all i0,(vi,vi+1)E. That is, p is an infinite path in G starting at vertex s. Since the set V of vertices is finite, every infinite trace of G must visit some vertices infinitely often. (a) If p is an infinite trace, let Inf(p)V be the set of vertices that occur infinitely often in p. Show that Inf(p) is a subset of a strongly connected component of G. (b) Describe an algorithm that determines if G has an infinite trace. (c) Describe an algorithm that determines if G has an infinite trace that visits some good vertex in VG infinitely often. (d) Describe an algorithm that determines if G has an infinite trace that visits some good vertex in VG infinitely often, but visits no bad vertex in VB infinitely often