Final answer:
The statement that Great Britain agreed to give Canada to the United States is false. The Treaty of Ghent restored pre-war boundaries between the US and Canada, and the British North American Act of 1867 joined British colonies into the autonomous Dominion of Canada within the British Empire.
Step-by-step explanation:
Great Britain did not agree to give Canada to the United States. Throughout history, including during the War of 1812 and the Treaty of Ghent, the United States and Great Britain had various disputes over territories, but Canada remained outside of American control and eventually formed its own self-governing Dominion within the British Empire. After the War of 1812, the Treaty of Ghent, signed in 1814, restored the boundaries between the United States and British Canada to their pre-war status. This outcome was favorable to the United States as it allowed for continued expansion into the West without conflict with Great Britain over Canadian territories.
Regarding the additional statements provided:
1. Both the Americans and the British did not give up claims to the Mississippi; therefore, this statement is false.
2. The Conciliatory Proposition did not lead to the mother country giving in to most of the American colonists' demands, which makes this statement false as well.
3. The Treaty of Paris signaled the end of the war and began a period of peace between the United States and Great Britain, but it was imperfectly applied and ignored American Indians, making the statement about ignoring American Indians true.
The British North America Act of 1867 joined British colonies into the Dominion of Canada, which was an important step towards Canada's independence, but it did not involve ceding Canada to the United States. Hence the statement is false.