Originally Posted by

**hatsoff** Well, we can put them into plain English:

**(a)** For every integer $\displaystyle a\geq 1$ there is an integer $\displaystyle b\geq 1$ with $\displaystyle ab=\frac{a}{b}$.

This is clearly true by choosing $\displaystyle b=1$ for any $\displaystyle a$.

**(b)** For every integer $\displaystyle b\geq 1$, there is an integer $\displaystyle a\geq 1$ with $\displaystyle ab=\frac{a}{b}$.

Now, regardless of $\displaystyle a$, it is clear that $\displaystyle b^2=1$. So if $\displaystyle b=2$ then (b) implies $\displaystyle 4=1$, which is a contradiction. So (b) is false.