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For \\(A=\\{a, b, c\\}\\) and \\(P=\\{1, 2\\}\\), the asignments \\(A_1=\\{a\\}, A_2=\\{b, c\\}\\) and \\(A_1=\\{b, c\\}, A_2=\\{a\\}\\) are different partitions in the book, but the corresponding equivalences are the same.
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