Final answer:
Historically, land disputes following Columbus's voyages were often settled through treaties, but without more context, true or false cannot be determined. Acquisition of land was a primary driver in early U.S. Indian policy. The British, not the Americans, gave up claims to the Mississippi after the American Revolution.
Step-by-step explanation:
The question addresses historical events and policies that were put in place during the era of colonization and the formation of United States policies. The question related to the conflicts over lands discovered by Christopher Columbus is referring to the actions taken historically to resolve territorial disputes following his voyages to the New World. These conflicts were often settled through treaties and agreements, although the question does not specify which specific incidents or resolutions it is referring to, hence we cannot assert if they 'tried to settle' such disputes as true or false without more context.
In regard to the statement that the acquisition of land was the most important motivating factor in the formulation of early U.S. Indian policy, historical records show that land acquisition was indeed a key driver behind the policies created during that time, meant to manage relations with Native American tribes and often leading to their displacement.
Regarding the claim that both the Americans and the British gave up claims to the Mississippi for peace, this is historically inaccurate. After the American Revolution, through the Treaty of Paris in 1783, Britain recognized American sovereignty and thus gave up claims to territories east of the Mississippi River. However, the Americans did not give up their claims; instead, the United States gained recognized control over the area.