For the purposes of this problem you dont really need to kno

For the purposes of this problem, you don’t really need to know what the Vertex Cover problem is, but if you are interested, it is described in the previous problem. Also, for the purposes of this problem, you should not assume anything other than what is stated in the problem. For example, you should not assume that the Vertex Cover problem or the Independent Set problem is in NP or is NP-hard. (a) Suppose we knew that • there is a polynomial-time reduction from Vertex Cover to Independent Set and • the Vertex Cover Problem cannot be solved in polynomial time. With these assumptions, indicate which of the following choices is the right one (you don’t have to give any explanations.) 1. We can’t say for sure whether or not Independent Set can be solved in polynomial time. 2. We know for sure that Independent Set can’t be solved in polynomial time. 3. We know for sure that Independent Set can be solved in polynomial time. (b) Suppose we knew that • there is a polynomial-time reduction from Vertex Cover to Independent Set and • the Vertex Cover Problem can be solved in polynomial time. With these assumptions, indicate which of the following choices is the right one (you don’t have to give any explanations.) 1. We can’t say for sure whether or not Independent Set can be solved in polynomial time. 2. We know for sure that Independent Set can’t be solved in polynomial time. 3. We know for sure that Independent Set can be solved in polynomial time.

Solution

(b) 1 st choice is the right one the anser is we can\'t say for sure wheather or not independent set can be solved in polynomial time