I am having a difficulty proving that the set splitting problem is NP-complete using SAT.
Suppose S = {1,2,3,4} and C is a collection of subsets of S, say C1 = {1,2}, C2 = {3,4}, C3 = {1,3,4}. Each number is given a color red or blue ... need to verify if none of the subsets have only one color.
How do I use SAT problem to prove this is NP-complete. I know that I should proceed by giving a color a value of either true or false. But how to use the SAT problem to show this. I just can't seem to understand how this will work. Can someone explain this concept to me?
