**Proof:** For all a ∊ A, we have (a, b) ∊ R.

Since R is symmetric, so (b, a) ∊ R

Now, (a, b) ∊ R and (b, a) ∊ R imply that (a, a) ∊ R.

Since R is transitive hence R is reflexive.

Therefore R is an equivalence relation. (**Proved)**

Home / Discrete mathematics / Let R be a symmetric and transitive relation on a set. Show that for every a in A there exist b in A such that (a, b) ∊ R then R is an equivalence relation.

Tags Discrete mathematics mathematics Symmetric relation Transitive relation

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