Final answer:
The statement about proprietors in a proprietary colony only collecting profits is false; they had additional governing responsibilities. Colonists did object to tax application without representation, which is true. The description of sharecroppers as tenants paying with crop shares is also true.
Step-by-step explanation:
The statement that in a proprietary colony, the Proprietors have no responsibilities except to collect the profits is false. Proprietors in these colonies were responsible for much more than just collecting profits. They basically owned the colony, having obtained their charter from the monarchy, and were responsible for governing the colony, which included making laws, appointing officials, and sometimes defending the colony from attacks or disputes. Proprietary colonies included places like Pennsylvania, Maryland, and Delaware during the colonial period in America.
Regarding taxation, it is true that the colonists did not necessarily object to the principle of taxation in itself, but they largely protested against how the tax money was being spent and they demanded representation in the decision-making process. This sentiment was famously encapsulated in the phrase 'no taxation without representation'.
When it comes to sharecroppers, the statement that they were tenant farmers who paid their rent with shares of their crops is also true. Sharecropping was a system that became widespread in the Southern United States during Reconstruction after the Civil War, where landlords allowed tenants to use their land in exchange for a portion of the crops produced on their portion of the land.