The set that is closed under addition and multiplication but not under subtraction or division is the natural numbers.
Here's why:
- Natural numbers (1, 2, 3, ...) are closed under addition (e.g., 2 + 3 = 5) and multiplication (e.g., 2 × 3 = 6), but they are not closed under subtraction (e.g., 2 - 3 is not a natural number) or division (e.g., 2 ÷ 3 is not a natural number).
The other sets mentioned (integers, rational numbers, irrational numbers, and real numbers) do not meet this criterion.