No code please, just explain. Thank you!

Question 3: Show that the following problems are in NP (this does not contains the harder part of showing that the problem is NPC. You only need to show that given a candidate solution, it is possible to check in polynomial time if the solution is valid) 1. The 3 coloring problem: Given a graph G can we give the numbers 1 or 2 or 3 to 2. The k-coloring problem. Given a graph and an input k (k can depend on n) is 3. Given an undirected graph G, does it has a path of length k or more so that all the vertices of the graph, so that neighbors get different numbers? the graph k-colorable? the vertices are different? 4. Given a graph G(V, E), a number k and a number t. Is there a subset U of V of size U k so that the number of edges with both endpoints in U is at least t? 5. Given a universe U, a collection of subsets s1, S2, . . . , Sm of U and a number k, is there a subcollection Sin . . . , Sik whose union s U? Namely U = -Si