Given a set $\{1,2,3,4\}$, how is the following relation $R$ antisymmetric?
$$R = \{(1, 2), (2, 3), (3, 4)\}$$
Note: Antisymmetric is the idea that if $(a,b)$ is in $R$ and $(b,a)$ is in $R$, then $a = b$. In my textbook it says the above is antisymmetric which isn't the case as whenever $(a,b)$ is in $R$, $(b,a)$ is not.