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What does the Closure Property tell you about the rational and irrational numbers under subtraction?(1 point)
Responses
The difference of a rational number and an irrational number will always be a rational number.
The difference of a rational number and an irrational number will always be a rational number.
The difference of two rational numbers will always be a rational number.
The difference of two rational numbers will always be a rational number.
The difference of a rational number and an irrational number cannot be determined.
The difference of a rational number and an irrational number cannot be determined.
The difference of two irrational numbers will always be an irrational number.
The difference of two irrational numbers will always be an irrational number.
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The difference of two rational numbers will always be a rational number.
Reason: The rational numbers are closed under subtraction (subtracting rationals gives a rational). The irrationals are not closed under subtraction (e.g., √2 − √2 = 0, which is rational), and subtracting a rational from an irrational always gives an irrational.
Reason: The rational numbers are closed under subtraction (subtracting rationals gives a rational). The irrationals are not closed under subtraction (e.g., √2 − √2 = 0, which is rational), and subtracting a rational from an irrational always gives an irrational.
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