Repeat Exercise 11, assuming R is symmetric and transitive but not reflexive.
Reference:
Let R be a relation on a set A that is reflexive and symmetric but not transitive. Let R(x) = {y: x R y}. [Note that R(x) is the same as x/R except that R is not an equivalence relation in this exercise.] Does the set {R(x): x ∈ A}always form a partition of A? Prove that your answer is correct.
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