40. Assume $P\ne NP$. For each of the following 10 problems, decide whether it is a P-problem, or an NP-hard (or NP-complete) problem, or neither. (1) Find a longest simple path between two nodes, where the given graph has positive edge weights. (2) Find a shortest simple path between two nodes in a directed graph with negative and/or positive edge weights, and containing negative weight cycles. (3) Find a negative weight directed cycle in a weighted directed graph. (4) Find a positive weight directed cycle in a weighted directed graph. (5) Find a largest cycle in a graph, where the edge-weight is 1 for each edge. (6) Find a smallest cycle in a graph, where the edge-weight is 1 for each edge. (7) Find a maximum cut in a flow network. (8) Find a minimum cut in a flow network. (9) Find a maximum independent set in a time interval graph. (10) The 2-CNF-Satisfiability problem.

Among, the above 10 problems, x of them are P-problem, y of them are NP-hard (or NP-complete), and z of them are neither. Find x, y, and z, then choose the following correct ones.