Let A1, A2, ..., An be a family of distinct finite sets of positive integers where n = m² +1. Show that there exist at least m +1 of these sets, say Ak, Ak 3 ..., Akm+1, such that Ak, U Ak, ordered set P = ({A1, A2,..., An}, C).) Ak does not hold for all distinct kr, ks, kt. (Hint: Consider the partially

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