What do you understand by dependency preservation?

Given a relation R and a set of FDs F, dependency preservation states that the closure of  the union of the projection of F on each decomposed relation Ri is equal to the closure of F. i.e.,

((P_R1(F))  U … U (P_Rn(F)))⁺ =  F⁺

 if decomposition is not dependency preserving, then some dependency is lost in the decomposition.