The sample space for the experiment is the set of all possible outcomes. In this case, the set of numbers to select from is {2, 3, 4, 5, 6, 7, 8, 9, 10}.
The event that covers the entire sample space is the one that includes all possible outcomes.
Out of the provided options:
A. "The number is greater than 2" includes {3, 4, 5, 6, 7, 8, 9, 10}, but it does not cover the entire sample space since it excludes the number 2.
B. "The number is neither prime nor composite" is a contradictory statement. All numbers are either prime or composite. This event does not cover the entire sample space.
C. "The number is even or less than 12" includes {2, 3, 4, 5, 6, 7, 8, 9, 10}, which is the same as the sample space, and thus it covers the entire sample space.
D. "The number is not divisible by 5" includes {2, 3, 4, 6, 7, 8, 9}, but it does not include the numbers 5 and 10. Hence, it does not cover the entire sample space.
Therefore, the correct answer is C. "The number is even or less than 12."