The correct response regarding the closure property of rational and irrational numbers under subtraction is:
The difference of a rational number and an irrational number cannot be determined.
Here's why:
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Rational Number - Rational Number: The difference of two rational numbers is always a rational number. (Closure property holds for rational numbers under subtraction.)
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Irrational Number - Irrational Number: The difference of two irrational numbers can be either rational or irrational, so it cannot be determined that it will always yield an irrational number.
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Rational Number - Irrational Number: The difference of a rational number and an irrational number is always irrational.
Thus, the difference between a rational number and an irrational number will always be an irrational number, but it cannot be determined under the closure property as rational.
If you choose the response carefully, the right one with regard to the closure property is concerning how the difference behaves based on these categories.