Let P be a set whose elements are sets. The notation US denotes the SEP set...

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Let P be a set whose elements are sets. The notation US denotes the SEP set {xx ES for some S € P}. This is read "the union of the sets S in P Given a set A, and a set PC P(A), the set P is a partition of A if • P, and • USA, and SEP • For any SEP and T€ P, if S T then SnT = 6 That is, P is a partition of A the empty set id not an element of P, the union of the sets S in P equals A, and the sets in P are pairwise disjoint. 2a. Is the set P = {SCR: there is a ze Z with S = (n, n+1]} a partition of R? 2b. Given a set A with |A| = n where n > 1, let Q = {PCP(A): (P is a partition of A) ^ (P = 2)} What is the cardinality of Q in terms of n? Let P be a set whose elements are sets. The notation US denotes the SEP set {xx ES for some S € P}. This is read "the union of the sets S in P Given a set A, and a set PC P(A), the set P is a partition of A if • P, and • USA, and SEP • For any SEP and T€ P, if S T then SnT = 6 That is, P is a partition of A the empty set id not an element of P, the union of the sets S in P equals A, and the sets in P are pairwise disjoint. 2a. Is the set P = {SCR: there is a ze Z with S = (n, n+1]} a partition of R? 2b. Given a set A with |A| = n where n > 1, let Q = {PCP(A): (P is a partition of A) ^ (P = 2)} What is the cardinality of Q in terms of n?

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2a P SER There is clearly Pis Since for 2b let a Denote a partition of A n n ton any nt 2 US SE... View the full answer