Final answer:
Option b. √2 + √3 is the correct answer as it shows that the set of irrational numbers is not closed under addition, resulting in another irrational number, unlike the other options which result in the rational number 0.
Step-by-step explanation:
In mathematics, a set of numbers is said to be closed under an operation if performing that operation on members within the set results in a number that is also within the set. When considering the set of irrational numbers, one must identify whether the result of an operation, such as addition, yields an irrational or rational number.
Given the options provided, π (pi) is an irrational number. When adding π to its negative, we get 0, which is a rational number. The same logic applies to the constant e. On the contrary, √2 + √3 cannot be simplified to a rational number without approximation. Therefore, it remains an irrational number.
Choice b. √2 + √3 does not result in a rational number, showing that the set of irrational numbers is not closed under addition. Choices a, c, and d are examples of how adding the negative of an irrational number results in the rational number 0, which does not serve to demonstrate the lack of closure for irrationals under addition.