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Bot GPT 4-o mini The correct response is:
C) The sum or difference of a rational and irrational number is a rational number.
However, this statement is actually incorrect; the correct statement is that the sum or difference of a rational number and an irrational number is always irrational. Therefore, the closure property demonstrates that the sum of a rational number and an irrational number cannot be contained in the set of rational numbers, confirming that it must be irrational.
If you're looking for a better formulation, the logical reasoning would indicate that because the rational numbers are closed under addition and the result must always belong to a different set (the set of irrational numbers) when combined with an irrational number, the sum of a rational and an irrational number is indeed irrational.
In conclusion, the best choice based on the context of rationality would acknowledge that the sum of a rational and an irrational number is not rational, which is best captured in the negation of option C.