Question
What does the Closure Property tell you about the rational and irrational numbers under subtraction?(1 point)
Responses
The difference of a rational number and an irrational number will always be a rational number.
The difference of a rational number and an irrational number will always be a rational number.
The difference of a rational number and an irrational number cannot be determined.
The difference of a rational number and an irrational number cannot be determined.
The difference of two rational numbers will always be a rational number.
The difference of two rational numbers will always be a rational number.
The difference of two irrational numbers will always be an irrational number.
Responses
The difference of a rational number and an irrational number will always be a rational number.
The difference of a rational number and an irrational number will always be a rational number.
The difference of a rational number and an irrational number cannot be determined.
The difference of a rational number and an irrational number cannot be determined.
The difference of two rational numbers will always be a rational number.
The difference of two rational numbers will always be a rational number.
The difference of two irrational numbers will always be an irrational number.
Answers
Answered by
GPT-4o mini
The correct statement regarding the closure property of rational and irrational numbers under subtraction is:
**The difference of two rational numbers will always be a rational number.**
Additionally, to clarify the other cases:
- The difference of a rational number and an irrational number will **always be an irrational number**.
- The difference of two irrational numbers can sometimes be rational (for example, \( \sqrt{2} - \sqrt{2} = 0 \), a rational number), but it can also be irrational, so it is not guaranteed to be irrational.
Thus, the closure property specifically confirms that the subtraction of two rational numbers results in a rational number.
**The difference of two rational numbers will always be a rational number.**
Additionally, to clarify the other cases:
- The difference of a rational number and an irrational number will **always be an irrational number**.
- The difference of two irrational numbers can sometimes be rational (for example, \( \sqrt{2} - \sqrt{2} = 0 \), a rational number), but it can also be irrational, so it is not guaranteed to be irrational.
Thus, the closure property specifically confirms that the subtraction of two rational numbers results in a rational number.