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10 Nov 2019
Please show me the process. Thank you !!!
Suppose A is a set. If F and G are partitions of A. then we'll say that F refines G if X F Y G(X Y). Let P be the set of all partitions of A, and let R = {(F, G) P times P F refines G}. Prove that R is a partial order on P. Suppose that S and T are equivalence relations on A. Let F = A/S and G = A/T. Prove that S T iff F refines G. Suppose F and G are partitions of A. Prove that F G is the greatest lower bound of the set {F, G} in the partial order R. See exercise 17 for the meaning of the notation used here.)
Please show me the process. Thank you !!!
Suppose A is a set. If F and G are partitions of A. then we'll say that F refines G if X F Y G(X Y). Let P be the set of all partitions of A, and let R = {(F, G) P times P F refines G}. Prove that R is a partial order on P. Suppose that S and T are equivalence relations on A. Let F = A/S and G = A/T. Prove that S T iff F refines G. Suppose F and G are partitions of A. Prove that F G is the greatest lower bound of the set {F, G} in the partial order R. See exercise 17 for the meaning of the notation used here.)
Bunny GreenfelderLv2
6 Feb 2019