Final answer:
If the switch reboots and all routers have to re-establish OSPF adjacencies, Router R3 will become the DR, and Router R2 will become the BDR.
Step-by-step explanation:
If the switch reboots and all routers have to re-establish OSPF adjacencies, the selection of the new DR (Designated Router) and BDR (Backup Designated Router) is based on the OSPF router priority value. The router with the highest priority becomes the DR, and the router with the second-highest priority becomes the BDR. If multiple routers have the same priority, the router with the highest router ID is elected as the DR.
In the given options, Router R3 has the highest priority value in all the routers, so it will become the DR. Among the other routers, Router R2 has the second-highest priority value, so it will become the BDR.
Therefore, the correct answer is Option D: Router R3 will become the DR, and Router R2 will become the BDR.