My book states that $A= \{(1, 2), (2, 1)\}$ isn't transitive.
It also states that $B=\{(2, 1), (1, 2)\}$ is transitive and symmetric but not reflective.
I think that $A = B$ thus this is a contradiction. I think this $A$ and $B$ are equivalent because these are unordered sets of ordered pairs.
Which is correct and if $B$ is incorrect then what is a transitive, symmetric but not reflexive set?
Clearly, $A\neq B$. However, it is true that both relations must have the same properties. What happens is that neither of them is reflexive or transitive and both of them are symmetric.