Final answer:
The claim that city-state borders changed, becoming bigger or smaller, is true. History shows that city-states evolved due to various factors like conquests, alliances, and treaties, affecting their size and borders.
Step-by-step explanation:
The statement that city-states grew bigger or smaller, and the borders kept changing is generally True. Historical evidence shows that the nature and size of city-states and their territories were subject to change due to various factors such as military conquest, political alliances, economic necessities, and social transformations. For example, the nation-states of western Europe which grew out of an assemblage of kingdoms and territories changed borders frequently over the centuries due to wars and treaties. Similarly, relations between Mexican city-states were complex, with alliances and marriages affecting political power and territorial control. The Roman Empire also experienced significant changes in its borders due to increased pressure from organized barbarian groups, ultimately contributing to the fragmentation of the western Empire.