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), {e, f}, {a)) Then, T = { {a, b, c), {c, d, e), {f, g)), since {a, 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 = { lover and S There exists a total union of size k or less) Show that: Vertex Cover Sp Total Union. 10]