Final answer:
The false statement about the Crisis of the Third Century is that both the Roman and Han Empires fell during this period. The Roman Empire faced many challenges, but it did not fall until later on.
Step-by-step explanation:
Regarding the Crisis of the Third Century for the Roman and Han Empires, the statement that is FALSE is D. Both empires fell. Although the Roman Empire faced severe strain during this period, with a high turnover of emperors, economic instability, and challenges from barbarian tribes, it did not actually fall at this time. In fact, the Roman Empire continued to exist, particularly in the East as Byzantium, until the end of the fifth century. Hence, during the third century, while the Western Roman Empire experienced significant fragmentation and decentralization of power, and while hostile neighbors did indeed take advantage of the Empire's instability, the entity of the Roman Empire endured beyond this period of crisis.