Final answer:
The claim that New York had fewer than 10,000 residents at the end of the French and Indian War is false, as the population figures during the post-war period leading up to the American Revolution were much higher.
Step-by-step explanation:
The statement 'There were fewer than 10,000 people living in New York when the French and Indian War ended' is false. After the French and Indian War, which ended in 1763, Great Britain's victory led to significant territorial expansion and the maintenance of a considerable military presence in North America to defend new borders and pacify relations with Native American tribes. By the American Revolution, the population of loyalists in the colonies was about 400,000, indicating that the population was already substantial during the period after the French and Indian War and before the Revolution. Hence, New York, being one of the significant colonies, would have had a population exceeding 10,000.