The correct response that relates to how the Closure Property proves that the sum of a rational and irrational number is irrational is:
The sum or difference of two rational numbers is a rational number.
To clarify: the Closure Property states that the sum (or difference) of two rational numbers is always a rational number. However, when you add a rational number to an irrational number, the result cannot be a rational number; if it were, it would contradict the definition of irrational numbers, as you can't express an irrational number as a simple fraction. Therefore, the sum of a rational number and an irrational number is always irrational.
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