Is ($ m \le n $ iff $\frac{n}{m}$ is an even integer) reflexive?

Question

On the domain $S = \{2,3,4,6,8,18,24\}$, consider the partial order: $ m \le n $ iff $\frac{n}{m}$ is an even integer.

Is the above relation reflexive and thus a partial order? I don't see how it's reflexive as $\frac{2}{2}=1$ and 1 is odd.

Answer 1

Your example is correct for showing that the relation is not reflexive. This is sufficient to conclude that the relation is not a partial order. Your language suggests that being reflexive is sufficient for the relation to be a partial order, which is not true. It needs to be antisymmetric and transitive as well.