This question is from the book Abstract Algebra: Theory and Applications by Thomas W. Judson.
Chapter 1 – Question 28
Find the error in the following argument by providing a counterexample. “The reflexive property is redundant in the axioms for an equivalence relation. If $x \sim y$, then $y \sim x$ by the symmetric property. Using the transitive property, we can deduce that $x \sim x$.”