Let $\approx$ be the relation on sets defined by $A \approx B$ if and only if there exists a bijection $f: A \to B$. Then $\approx$ is reflexive, symmetric, and transitive: for every set $A$ one has $A \approx A$; for all sets $A$ and $B$, if $A \approx B$, then $B \approx A$; and for all sets $A$, $B$, and $C$, if $A \approx B$ and $B \approx C$, then $A \approx C$.