Answer:
3
Step-by-step explanation:
Obviously, since the set must have at least 3 cities, this number has to be at least 3, but if the government is lucky enough to choose the first 3 cities that by any chance are all mutually disconnected, then the set meets the requirements (3 cities that either are all mutually connected by road OR they all are mutually disconnected).
The probability of choosing at random 3 cities that are all mutually disconnected by road might be small, but it is not zero, so the answer is:
The minimum number of cities that the government needs to pick is 3.
