2. Consider the Total-Union problem: given sets U and S, where S is a set of subsets of U, find a smallest subset of S, denoted by T, such that the union of all the elements of T equals U. It sounds more complicated than it is. Here's an example, let U={a, b, c, d, e, f,g) S = {{a, b, c), {b, d), {f,g), fe,g), {c,d,e), fe, f),(a)) Then, T = {{a, b, c), {c, d, e), {f,g)), since ta, b,c) U {c,d,e) U {f,g) = U and there does not exist a two element subset of S such that said subset is a total union. Let Total Union = { |Over U and S There exists a total union of size k or less) Show that: Vertex Cover