Final answer:
Most Indian tribes sided with the British during the American Revolution fearing land loss, which is true. The Americans gained rights to the Mississippi in the Treaty of Paris, making the statement about both sides giving up claims false. Harrison's victory in 1840 was for the Whig Party, not the Democrats, also false.
Step-by-step explanation:
The notion that most Indian tribes and nations supported the British during the American Revolution is typically regarded as true. They were concerned that an American victory would lead to further expansion and loss of their lands. In contrast, the claim that both the Americans and the British gave up claims to the Mississippi River for the sake of peace is false; in the Treaty of Paris 1783, Great Britain recognized American rights to the territory east of the Mississippi River. Lastly, William Henry Harrison's defeat over Martin Van Buren marked a victory for the Whig Party, not the Democratic Party, thus this statement is false.