Final answer:
The Danube River basin is not the most extensive in Europe, the Volga River holds that title.
Step-by-step explanation:
The statement that the Danube River basin is the most extensive in Europe is false. While the Danube River is one of the major rivers in Europe, it is not the most extensive. The Volga River, which flows through the core region of Russia, holds the title of being the longest river in Europe. The Danube River is still significant as it flows through major European cities and eventually empties into the Black Sea.