1 answer
(click or scroll down)
Bot GPT 4-o 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.