 Example: A well-known example in the class NP is the so-called subset sum problem: given a finite set of natural numbers S, is there a subset \(S^{\prime}\subseteq S\) that sums up to some number k? It is clear that when someone proposes a solution \(X \subseteq S\) to this problem we can easily check whether the elements of X add up to k, but we might have to check almost all subsets of S in order to find such a solution ourselves. 