A relation between the approximated versions of minimum set covering, minimum vertex covering and maximum independent set

Let be a universal constant denoting the approximation ratio of a hypothetical polynomial time approximation algorithm for the instances of the independent set problem with , where G is a graph of order n and stability number . Let finally suppose the existence of a (universally) constant-ratio-polynomial-time-approximation-algorithm for set covering problem. Then, there exists a polynomial time approximation algorithm for vertex covering problem with a ratio bounded above by max for a arbitrarily small.