She is incorrect with her statement.
We know that a product of two rational numbers is always a rational number no matter they are positive or negative.
Whereas the product of a non-zero rational number and a irrational number is always a irrational number.
The example which contradicts her statement is:
If we consider a positive rational number as: 3
and a negative ration number as: -2
The there product i.e.
3×(-2)= -6 which is again a rational number.
In a nutshell, the Product of a positive and a negative Rational Number is always Rational, since a Rational Number exist.
A Rational Number is a Real Number of the form:
[tex]x = \frac{a}{b}[/tex], [tex]a\in \mathbb{Z}[/tex], [tex]b \in \mathbb{Z} - \{0\}[/tex], [tex]x \in \mathbb{R}[/tex] (1)
Where:
Given two Rational Numbers, its Product will be always a Rational Number.
[tex]x_{1}\cdot x_{2} = \left(\frac{a}{b} \right)\cdot \left(-\frac{c}{d} \right)[/tex]
[tex]x_{1}\cdot x_{2} = -\frac{a\cdot c}{b\cdot d}[/tex]
In a nutshell, the Product of a positive and a negative Rational Number is always Rational, since a Rational Number exist.
Please see this question related to Irrational Numbers: https://brainly.com/question/528650
