A) OSPF is based on distance-vector routing protocol.(B) Both link-state and distance-vector routing are based on the least cost goal.(C) BGP4 is based on the path-vector algorithm.(D) The three-node instability can be avoided using split horizon combined with poison reverse.(E) RIP is based on link state algorithm.

A) False. OSPF (Open Shortest Path First) is based on a link-state routing protocol, not a distance-vector routing protocol. It uses Dijkstra's algorithm to calculate the shortest path.

B) True. Both link-state and distance-vector routing protocols aim to find the least cost path. Link-state protocols have a complete view of the network topology, while distance-vector protocols only know about their neighbors.

C) True. BGP4 (Border Gateway Protocol version 4) is based on the path-vector algorithm. It is an extension of the distance-vector routing protocol, with additional path attributes for more complex routing decisions.

D) True. The three-node instability problem, also known as count-to-infinity, can be mitigated using techniques like split horizon and poison reverse. Split horizon prevents a router from advertising a route back to the router from which it was learned. Poison reverse takes this a step further by actively advertising the route as unreachable.

E) False. RIP (Routing Information Protocol) is based on a distance-vector algorithm, not a link-state algorithm. It uses hop count as a routing metric.