What is wrong with the following argument, which supposedly shows that any relation R on X that is symmetric and transitive is reflexive?
Let x ϵ X. Using symmetry, we have (x, y) and (y, x) both in R. Since (x, y), (y, x) ϵ R, by transitivity we have (x, x) ϵ R. Therefore, R is reflexive.
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