According to the statement, was the result positive always?

19 Views Asked by At

The expression:

$\dfrac{r}{pq}$, with $r$, $p$ and $q$ integers and ($p$ and $q$) $\neq 0$,

is positive if:

$$\frac{r}{p} > 0 \text{ and } q > 0 \tag 1$$

True, $\frac{r}{p} \cdot \frac{1}{q}$ because $\text{positive} \times \text{positive}$ is always positive

$$pq < 0 \text{ and } r \tag 2$$ not positive

True, because $\frac{r}{1} \cdot \frac{1}{pq}$ and $\text{negative} \times \text{negative}$ is always positive.

My problem is that the correct answer is only I, so what am I failing to think that the second is correct?