Let $R$ be a symmetric, transitive relation. If $(x, y) \in R$ then the symmetric property implies that $(y, x) \in R$. Using the the transitive property upon $(x, y)$ and $(y, x)$ we can conclude $(x, x) \in R$. Is this fair logic or is it flawed?
Fake proof, symmetric and transitive relation is already reflexive
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discrete-mathematics
relations
fake-proofs