Question: Let S be a finite set with |S| = N and let c1, c2, c3, c4 be four conditions, each of which may be satisfied

Let S be a finite set with |S| = N and let c1, c2, c3, c4 be four conditions, each of which may be satisfied by one or more of the elements of S. Prove that N(234) = N(c1234) + N(1234).

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