Symmetric property of an equivalence relation states that if $a$~$b$ then
$b$~$a$; Transitive property states that if $a$~$b$ and $b$~$c$ then $a$~$c$.
What is wrong with the following proof that symmetric and transitive property
imply reflexive property ? Let $a$~$b$; then $b$~$a$, whence, by property of transitivity
(using $a = c$), $a$~$a$.(,where '~' denotes a binary relation ).
Is there any alternative of reflexive property which will insure that properties of symmetricity and transitivity imply property of reflexivity ?