The byzantine empire replaced the western roman empire after the fall of rome. true false

Replaced how?  If you mean like the Roman empire, that would be incorrect.  Both empires considered each other Roman and both empires considered themselves Roman.  So when the west fell, the Byzantines did not 'replace' the western Romans in being Roman. Instead, they just kept on being Roman as their western counterparts fell.  However, for a period, the Byzantines did manage to reconquer parts of the Western Empire and even Rome, but that was relatively short-lived.  In that case, you could argue that the Byzantines sort of did replace the western Romans in being the Roman empire with Rome in its possession. However, that is a stretch in my opinion. 

In short: False, the Eastern Romans did not replace the western Romans as they were both seen as Romans, just with different governments.