# Question: Suppose that each of the elements of S 1

Suppose that each of the elements of S = {1, 2, . . . , n} is to be colored either red or blue. Show that if A1, . . . ,Ar are subsets of S, there is a way of doing the coloring so that at most

of these subsets have all their elements the same color (where |A| denotes the number of elements in the set A).

of these subsets have all their elements the same color (where |A| denotes the number of elements in the set A).

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