  In this paper we prove that if $A$ and $B$ are infinite subsets of positive
integers such that every positive integer $n$ can be written as $n=ab$, $a\in
A$, $b\in B$, then $\displaystyle \lim_{x\to \infty}\frac{A(x)B(x)}{x}=\infty
$. We also prove many other results about sets like this.
