Understanding symmetric and antisymmetric relations

Question

I'm having an issue working out if the following is just antisymmetric or antisymmetric and symmetric

$\{(1,1),(2,2),(3,3)\}$

I'm certain its antisymmetric but im just not certain if the rule

$R$ is symmetric if whenever $(a, b)\in R$ then $(b, a) \in R$.

applies when $a=b$. Thanks for any help.

Answer 1

Symmetric means if $(1,2) \in R$, then $(2,1) \in R$. In your example, all elements are of the form $(1,1)$ so it is true.