The router that runs OSPF first enters the Full state and then synchronizes the LSDB.

The statement is incorrect. The OSPF neighbor state machine proceeds through several stages before reaching the final Full state. LSDB (Link-State Database) synchronization occurs during the Exchange and Loading states, which precede the Full state. In the Exchange state, routers exchange Database Description (DBD) packets. In the Loading state, they request and receive any missing or updated LSAs. The transition to the Full state only happens after the LSDBs are completely synchronized, signifying the completion of the process.

The question is a True/False statement. The statement is false because it reverses the sequence of events. LSDB synchronization is a prerequisite for, not a consequence of, entering the Full state.

Huawei. (2020). HCIA-Datacom V1.0 Training Material. Section: OSPF Basics, Subsection: OSPF Neighbor States. The material details the state progression: ExStart -> Exchange -> Loading -> Full, and explicitly states that LSDB synchronization happens in the Exchange and Loading states before the Full state is achieved.

Moy, J. (1998). RFC 2328: OSPF Version 2. Section 10: The Neighbor State Machine. This foundational document describes the state transitions, clearly indicating that the Loading state (where LSDBs are synchronized via Link State Request and Update packets) must be completed before the neighbor is considered fully adjacent (Full state).