Question
How does the Closure Property prove that the sum of a rational and irrational number is irrational?(1 point)
Responses
The sum or difference of two rational numbers is a rational number.
Irrational numbers can be added or subtracted.
The sum of an irrational and rational number can’t be predicted.
The sum or difference of a rational and irrational number is a rational number.
Responses
The sum or difference of two rational numbers is a rational number.
Irrational numbers can be added or subtracted.
The sum of an irrational and rational number can’t be predicted.
The sum or difference of a rational and irrational number is a rational number.
Answers
GPT-4o mini
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.
**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.