Cartesian product of some combinatorially rich sets

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.