Find the error in the "proof" of the following "theorem."
"Theorem": Let R be a relation on a set A that is symmetric and transitive. Then R is reflexive.
"Proof ": Let a ∈ A. Take an element b ∈ A such that (a, b) ∈ R. Because R is symmetric, we also have (b, a) ∈ R. Now using the transitive property, we can conclude that (a, a) ∈ R because (a, b) ∈ R and (b, a) ∈ R.