Final answer:
Sharecroppers were indeed tenant farmers who paid rent through a portion of their crops, and this statement is true. However, the claim that proprietors in proprietary colonies had no responsibilities besides profit collection is false. Also true is the fact that cotton continued to be a strong economic basis for the South during Reconstruction.
Step-by-step explanation:
The statement that sharecroppers were tenant farmers who paid their rent with shares of their crops is true. Sharecropping was a system that emerged during the Reconstruction era in the American South. Under this system, freed slaves and poor white farmers rented small plots of land from a landowner in exchange for a portion of their crop yield, which served as payment for rent.
Regarding proprietor colonies, the notion that the Proprietors have no responsibilities except to collect the profits is false. Proprietors in proprietary colonies had several responsibilities, including the governance of the colony and ensuring that it was productive and profitable, not just for themselves but also for the settlers.
Lastly, the statement that Cotton formed a strong economic basis for the South during Reconstruction is true. After the Civil War, cotton remained a key crop for the southern economy and played a significant role in the South's recovery.