1. define independent-set as the problem that takes a graph g and an integer k and asks whether g contains an independent set of vertices of size k. that is, g contains a set i of vertices of size k such that, for any v and w in i, there is no edge (v, w) in g. show that independent-set is np-complete.

Answer the following questions regarding your system by using the commands listed in this chapter. for each question, write the command you used to obtain the answer. a. what are the total number of inodes in the root filesystem? how many are currently utilized? how many are available for use? b. what filesystems are currently mounted on your system? c. what filesystems are available to be mounted on your system? d. what filesystems will be automatically mounted at boot time?