Suppose there are n locations in a city which only has one-way roads. For each pair of locations, there is exactly one road between them (so for any pair of locations u,v, there is either a road from u to v, or a road from v to u, but not both). A nexus is a location which can be reached from any location in the city, using no more than 2 roads. Use induction to prove that there must be a nexus. Hint: Think about the set S, of cities which can reach nexus b using exactly 1 road, and explicitly refer to this set in your proof