An approximate algorithm for solving the node cover problem of a graph G = (V, E) is given as follows. Let N denote the solution (node cover). Initially, F = E. Arbitrarily select an edge e = (u,v) F, next add nodes u and v into N. Then remove all edges incident to u or v from F. Repeat the above procedure until F becomes empty. Suppose that P is the optimal solution (node cover). Show that |N| 2|P|.