\(\sc{VERTEX}\ \sc{COVER}\ \) Given a graph \(G = \langle V,E \rangle\) and a natural number \(k \leq \lvert V\rvert\), does there exist a set of vertices \(V' \subseteq V\) of cardinality \(\leq k\) such that for each edge \(\langle u,v \rangle \in E\), at least one of \(u\) or \(v\) is a member of \(V'\)?