The SATISFIABILITY problem is, given a collection of clauses, such as, {(x1 V x2 V x3 V x4), (x2 V x3 V x1), (x1 V x4)} assign values to all x; such that each clause evaluates true. This problem reduces to 3-SAT, where each clause has exactly three literals. (a) Show how a single clause that is not in the proper 3-SAT form is made by the reduction into several clauses each in proper 3-SAT. In particular, show the reduction for the following clause: x1 V x2 V x3 V x V x V x6 Name by y; any new variables introduced. (b) Why does your reduction work? Why is the reduced collection of clauses simultaneously satisfiable if and only if the original clause is satisfiable?