Question 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 (wt, Xj, yk, zt), 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

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Transcribed Image Text: 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 (wt, Xj, yk, zt), 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
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Transcribed Image Text: 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 (wt, Xj, yk, zt), 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