4. Which of the following problems are in P? Which of the following problems are in NP? Which of the following problems are NP-Hard? Justify your answers. For parts (a) and (b) we reference the problem of graph coloring. A graph coloring is a way of assigning a color to each vertex such that no two adjacent vertices have the same color. A graph is said to be k-colorable if there is a valid graph coloring which uses no more than k colors. As an example, all bipartite graphs are 2-colorable Using these definitions we define the following class of languages: k-COLORING = {G | G is a k-colorable graph) (a) 2-COLORING (b) 3-COLORING (c) LHaLT