Q:

Is this set Reflexive, Symmetric or Transitive?

Given the set:
$$R = \{(x,y)\;|\;x\times y \leq 2015 \;\;\text{and}\;\; x,y \subset \Bbb N \setminus \{0\}\}$$
Would this set be just symmetric as I think? Or am I misunderstanding set relations?

A:

Of all listed properties, this $R$ (considered as a binary relation on $\Bbb N\setminus\{0\}$, I suppose) is only symmetric (which it is because multiplication is commutative). It is not reflexive because $(45,45)\notin R$.
It is not transitive, for example because $(1000,2)\in R$ and $(2,100)\in R$, but $(1000,100)\notin R$.

