Private approximation, introduced by Feigenbaum, Ishai, Malkin, Nissim, Strauss, and Wright, a
llows us to find approximate solutions with disclosing as little information as possible. 
In STOC 2006, Beimel, Carmi, Nissim, and Weinreb studied the private approximation for both the vertex 
cover and the max exact 3SAT problems.
In this paper, we consider the set cover problem where the costs of all sets are polynomially bounded. 
We show that there exists neither a deterministic nor a randomized private approximation. 
We also consider the case that the frequencies of all elements are equal. 
We show that in this case there exist no deterministic private approximation.