Answer
Negation: "There exists a least positive rational number."
Proof: There is no least positive rational number.
Suppose there is a positive rational number $r$ such that, for all positive rational numbers $q$, $r\leq q$. Beginning with the trivial statement $1\lt2$, we can multiply both sides by $r$ to get $r\lt2r$ and then divide both sides by $2$ to get $\frac{r}{2}$
Work Step by Step
We can derive $r\lt2r$ from $1\lt2$ and $\frac{r}{2}$