Let F={A(i):1it, t2}, be a finite collection of finite, pairwise disjoint subsets of Z+. Let SR\{0} and AZ+ be finite sets. Denote by SA={i=1asi:aA, SiS, the si are not necessarily distinct}. For S and F as above we say that S is F-free if for every A(i), A(j)F, ij, SA(i)SA(j)=ϕ.We prove that for S and F as above, S contains an F-free subset Q such that |Q|c(F)|S|, when c(F) is a positive constant depending only on F.This result generalizes earlier results of Erdos [3] and Alon and Kleitman [2], on sum-free subsets. Several possible extensions are also discussed.