Let's examine the set {10, 11, 12, 13, ...} closely.
1. Identify the type of numbers in the set:
- The set starts at 10 and includes every subsequent integer.
- Therefore, it includes numbers like 10, 11, 12, 13, 14, and so on, extending infinitely.
2. Determine the properties of the numbers in the set:
- These numbers are positive integers.
- Since they start from 10 and include every positive integer greater than or equal to 10, we can classify them as a subset of the natural numbers.
3. Evaluate each option:
- Option A: The numbers ten, eleven, twelve, and thirteen.
- This option only lists the first four elements of the set, not all elements.
- Option B: All natural numbers greater than 9.
- This implies that the set includes 10 and every positive integer greater than 10, which matches our set.
- Option C: All rational numbers greater than 9.
- Rational numbers include fractions and decimals, not just integers. Thus, this option does not match our set.
- Option D: All natural numbers greater than 10.
- This starts at 11, not 10, and therefore does not include all elements of our set.
Given this analysis, the correct answer is:
B. All natural numbers greater than 9.
