The correct answer is false.
It is false that since the beginnings of colonization, the Navy of North Carolina had allowed African Americans to serve.
The Navy of North Carolina played an important role during the American Revolutionary War although they only have few ships. The Navy initiated operations in 1776 and ended operations in 1779. It all started when the Council of Safety of North Carolina authorized on December 21, 1775, the purchase of three ships. But the Navy of North Carolina did not allow African Americans to serve since the beginnings of colonization.
