1. 120 points] CLRS 34.3-2: Show that the Sp relation is a transitive relation on languages. That is, show that f L1 Ep L2 and L2 Sp L3, then L1 SP L3. 2. [20 points] Recall the definition of a complete graph Kn is a graph with n vertices such that every vertex is connected to every other vertex. Recall also that a clique is a complete subset of some graph. The graph coloring problem consists of assigning a color to each of the vertices of a graph such that adjacent vertices have different colors and the total number of colors used is minimized. We define the chromatic number of a graph G to be this minimum number of colors required to color graph a graph G is no less than the size of the maximal clique of G. G. Prove that the chromatic number of