show that the problem is in NP or explain why you think the problem is not in NP:

Maximum clique size: Recall that a clique is a set of vertices V such that every pair of vertices in V are adjacent to each other. Given a graph G and a natural number k in N$,$ is the size of the largest clique in G equal to k$?$

Note: For these problems, nk is not polynomial time as k may depend on n$.$

Note: For each of these problems which you believe is not in NP$,$ you should explain why it is difficult to verify a yes answer.