  Let $X$ be a nonempty set and $X^{2}$ be the Cartesian square of $X$. Some
semigroups of binary relations generated partitions of $X^2$ are studied. In
particular, the algebraic structure of semigroups generated by the finest
partition of $X^{2}$ and, respectively, by the finest symmetric partition of
$X^{2}$ are described.
