Final answer:
The Americans and the British did not give up claims to the Mississippi for the sake of peace.
Step-by-step explanation:
The statement, 'Both the Americans and the British gave up claims to the Mississippi for the sake of peace' is false.
After the French and Indian War, Britain claimed a vast expanse of territory that extended from Canada to Florida. However, much of this land was still under the control of native confederacies. Great Britain maintained troops in North America to defend its borders. The British government encouraged the Indians to resist American settlement and made it difficult for American merchants to trade with the British West Indies.
Additionally, Spain claimed the Tennessee River as the border between the United States and New Spain, and closed the Mississippi to American traffic. Spanish agents even encouraged settlers in Kentucky and Tennessee to break away from the United States.