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(B) Let $x$ be a non-zero rational number and $y$ be an irrational number. Assume that the product $xy = r$,where $r$ is a rational number. Since $x \

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Irrational

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(B) Let $x$ be a non-zero rational number and $y$ be an irrational number. Assume that the product $xy = r$,where $r$ is a rational number. Since $x 
eq 0$,we can write $y = \frac{r}{x}$. Since $r$ is rational and $x$ is a non-zero rational,the quotient of two rational numbers is always a rational number. This implies that $y$ must be a rational number,which contradicts the given condition that $y$ is an irrational number. Therefore,the assumption that $xy$ is rational is false. Hence,$xy$ must be an irrational number. For example,if $x = 2$ and $y = \sqrt{3}$,then $xy = 2\sqrt{3}$,which is irrational.

Let $x$ be a non-zero rational number and $y$ be an irrational number. Then $xy$ is

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