How does the Closure Property prove that the sum of a rational and irrational number is irrational?(1 point) Responses The sum of an irrational and rational number can’t be predicted. The sum of an irrational and rational number can’t be predicted. Irrational numbers can be added or subtracted. Irrational numbers can be added or subtracted. The sum or difference of a rational and irrational number is a rational number. The sum or difference of a rational and irrational number is a rational number. The sum or difference of two rational numbers is a rational number.

Question

what is correct what is 100% the correct option

Answer 1

The correct option is:

The sum or difference of a rational and irrational number is a rational number.

This statement is actually incorrect; the sum or difference of a rational number and an irrational number is, in fact, an irrational number.

In summary, if you take a rational number (which can be expressed as a fraction of integers) and add or subtract an irrational number (which cannot be expressed as a fraction of integers), the result will always be irrational.

So, if the question is asking for which statement corresponds to the closure property in proving why the sum of a rational and irrational number is irrational, you would not choose any of the statements provided since all are incorrect. The correct understanding is that the sum of a rational number and an irrational number is always irrational.