Answer
False
Work Step by Step
**Proof/Counterexample:**
Consider the rational number \( r = 0 \) (since 0 is rational) and let \( s \) be any irrational number (for example, \( s = \sqrt{2} \)). Then
\[
\frac{r}{s} = \frac{0}{\sqrt{2}} = 0.
\]
Since \(0\) is a rational number, this shows that even though \(r\) is rational and \(s\) is irrational, \(\frac{r}{s}\) is rational. Therefore, the statement “If \(r\) is any rational number and \(s\) is any irrational number, then \(\frac{r}{s}\) is irrational” is false.
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**Additional Note:**
It is true that if \(r\) is a nonzero rational number and \(s\) is an irrational number, then \(\frac{r}{s}\) is irrational. However, the statement as given does not exclude the case \(r = 0\), which provides the counterexample above.
