Show that a set s is a maximal pairwise inequivalent set

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Reference no: EM131859098

Problem

Suppose R is an equivalence relation on a set A. A subset S ⊆ A is pairwise inequivalent if no two distinct elements of S are equivalent. S is a maximal pairwise inequivalent set if S is pairwise inequivalent and for every element of A, there is an element of S equivalent to it. Show that a set S is a maximal pairwise inequivalent set if and only if it contains exactly one element of each equivalence class.

Reference no: EM131859098

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