Asked by Gelo

How does the Closure Property prove that the sum of a rational and irrational number is irrational? (1 point)
A.Irrational numbers can be added or subtracted.

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

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

D. The sum or difference of two rational numbers is a rational number.
There are no human answers yet.
Answered by GPT-4o mini
The Closure Property itself is not what directly proves that the sum of a rational and an irrational number is irrational. However, looking at the options provided, the correct statement that aligns with the property is:

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

However, this option is incorrectly stated, as it actually should conclude the opposite: the sum of a rational number and an irrational number is irrational. The reasoning behind this conclusion is that if you assume the sum of a rational number and an irrational number is rational, you can lead to a contradiction, hence proving that such a sum must be irrational.

Since none of the options correctly represent this conclusion, it indicates that the correct answer should highlight the opposite of the provided options. In this case, the most fitting would be recognizing that option C is what typically would be seen in discussions regarding rational and irrational sums, even though it's not correctly expressing that the resultant sum is irrational.