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Let R be a relation on a set that is reflexive and symmetric but not transitive?...

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Advance Math

Let R be a relation on a set that is reflexive and symmetric butnot transitive? Let R(x) = {y : x R y}. [Note that R(x) is the sameas x / R except that R is not an equivalence relation in thiscase.] Does the set A = {R(x) : x ∈ A} always/sometimes/never forma partition of A? Prove that your answer is correct. Do not proveby examples.

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