  We prove in this article the surjectivity of three maps. We prove in Theorem
$1.6$ the surjectivity of the Chinese remainder reduction map associated to the
projective space of an ideal with a given factorization into ideals whose
radicals are pairwise distinct maximal ideals. In Theorem $1.7$ we prove the
surjectivity of the reduction map of the strong approximation type for a ring
quotiented by an ideal which satisfies unital set condition. In Theorem $1.8$
we prove for Dedekind type domains which include Dedekind domains, for $k\geq
2$, the map from $k$-dimensional special linear group to the product of
projective spaces of $k$ mutually co-maximal ideals associating the $k$-rows or
$k$-columns is surjective. Finally this article leads to three interesting
questions $[1.9, 1.10, 1.11]$ mentioned in the introduction section.
