57. Suppose a set of routers all use the split-horizon technique; we consider here under what circumstances itmakes a difference if they use poison reverse in addition. (a) Show that poison reverse makes no difference in the evolution of the routing loop in the two examples described in Section 3.4.2, given that the hosts involved use split horizon. (b) Suppose split-horizon routers A and B somehow reach a state in which they forward traffic for a given destination X toward each other. Describe how this situation will evolve with and without the use of poison reverse. (c) Give a sequence of events that leads A and B to a looped state as in (b), even if poison reverse is used. Hint: Suppose B and A connect through a very slow link. They each reach X through a third node, C, and simultaneously advertise their routes to each other