Consider the following decision problem: Path Selection INSTANCE: A directed graph G = (V;E); a set S = {P1; P2;...; Pc} of c directed paths in G; a bound K >= 0. QUESTION: Is there a subset S'(S' is a subset in S) of cardinality S' >= K such that every pair of distinct paths from S' is node disjoint? A. Define the corresponding language, call it PS. B. Show that PS is NP. C. Give a polynomial-time reduction of 3-CNF-SAT to PS. D. Conclude that PS is NP-complete.