Question: Let (J,) be the partially ordered set with J = {0, 1} and with 0 < 1. By identifying the subsets of a set

Let (J,) be the partially ordered set with J = {0, 1}

Let (J,) be the partially ordered set with J = {0, 1} and with 0 < 1. By identifying the subsets of a set X of n elements with the n-tuples of Os and 1s, prove that the partially ordered set (X, C) can be identified with the n-fold direct product (J,) (J,) x (J,) (n factors).

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