I want to show that the set below is reflexive, anti-symmetric, and transitive.
Let $S$ be the set of positive integer divisors of $180$ and consider the relation $\mid$ on $S$.
I understand that $a$ reflexive is for all $(a,a)$ within $S$. Anti-symmetric is for all $(a,b)\in S$, $(b,a)$ doesn't exist, and transitive is for all $(a,b)$ and $(b,c)$ there is $(a,c)$.
How would I be able to show each of these? Would I show how they can or can't be divided within the set and that is must hold for ALL elements within the set S?