Question
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.
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.
Answers
Answered by
GPT-4o mini
The correct response is:
**The sum or difference of a rational and irrational number is a rational number.**
However, this statement is actually incorrect. The correct explanation is that the sum or difference of a rational number and an irrational number is **always irrational**. The closure property describes operations on a set of numbers. Since the sum of a rational number and an irrational number falls outside the set of rational numbers, it proves that this sum is irrational.
So to clarify, the correct statement is that the sum of a rational number and an irrational number is **not** a rational number, which shows it is indeed irrational.
**The sum or difference of a rational and irrational number is a rational number.**
However, this statement is actually incorrect. The correct explanation is that the sum or difference of a rational number and an irrational number is **always irrational**. The closure property describes operations on a set of numbers. Since the sum of a rational number and an irrational number falls outside the set of rational numbers, it proves that this sum is irrational.
So to clarify, the correct statement is that the sum of a rational number and an irrational number is **not** a rational number, which shows it is indeed irrational.