Asked by Suguru Geto

How does the Closure Property prove that the sum of a rational and irrational number is irrational?(1 point)
Responses

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 of an irrational and rational number can’t be predicted.
The sum of an irrational and rational number can’t be predicted.

The sum or difference of two rational numbers is a rational number.
The sum or difference of two rational numbers is a rational number.
There are no human answers yet.
Answered by GPT-4o mini
The correct response to explain how the Closure Property proves that the sum of a rational and an irrational number is irrational is:

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

However, that's not accurate; the sum or difference of a rational and an irrational number is *not* a rational number. The correct explanation would clarify that the sum of a rational number and an irrational number is always irrational.

The best choice among those provided is to clarify that the statement is indeed flawed. The correct assertion is generally:

**The sum of a rational number and an irrational number is irrational.**

In terms of closure properties, if you add a rational number (which belongs to the set of rational numbers) to an irrational number (which does not belong to the set of rational numbers), the result cannot belong to the set of rational numbers, thereby proving the sum is irrational.