  N. Hindman and D. Strauss had shown that, for discrete semigroups, the
cartesian product of two central sets are central. They also proved that the
product of J- sets and C-sets are also J-set and C-set and characterized when
the infnite product of these sets are preserved. To prove these results they
used the algebraic structure of Stone-Cech compactification of discrete
semigroups. In this work we will give a combinatorial proof of the preserveness
of those large sets under fnite cartesian product.
