How does the Closure Property prove that the sum of a rational and irrational number is irrational?(1 point)

The correct response is:

**The sum or difference of two rational numbers is a rational number.**

To explain further: If you have a rational number \( r \) (which can be expressed as \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \)) and an irrational number \( i \), then the sum \( r + i \) cannot be expressed in the same form as the rational number and remains irrational. This is because if \( r + i \) were rational, then you could subtract \( r \) to isolate \( i \), suggesting that \( i \) would be rational, which contradicts its definition. Hence, the conclusion is that the sum of a rational and an irrational number is irrational.