Since the 3-Dimensional Matching Problem is NP- complete, it is natural to expect that the corresponding 4-Dimensional Matching Problem is at least as hard. Let us define 4-Dimensional Matching as follows. Given sets W , X , Y , and Z , each of size n, and a collection C of ordered 4-tuples of the form (wi, xj, yk, zl), do there exist n 4-tuples from C so that no two have an element in common? Prove that 4-Dimensional Matching is NP-Complete.