Final answer:
The Eastern half of the Roman Empire separated and outlasted the Western half.
Step-by-step explanation:
The relationship between the Western Roman Empire and the Byzantine Empire can be best summarized as follows:
b) The Eastern half separated and outlasted the Western half.
After the fall of the Western Roman Empire, the Byzantine Empire, located in the Eastern half, continued to exist for another 1,000 years. It maintained many aspects of Roman traditions while also introducing new innovations in architecture, science, religion, and learning. The two empires had distinct cultural and religious differences, with the Byzantine Empire primarily speaking Greek and being influenced by Eastern Christianity.