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Collection of subsets for equivalence relations

Let S be a collection of subsets of X, X = US. [S is not necessarily peicewise disjoint.] xRy if x, y Є S ⊂ S. Is R necessarily an equivalence relation? Show why or why not.

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A collection of subsets for equivalence relations is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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