Show that strict preference ordering is not reflexive
Just think about the definition of $\succ$ (in terms of $\succeq$) and the result follows immediately.

Proof:
Suppose $x\succ x$. Then, by definition, $x\succeq x$ and $x\nsucceq x$, which is impossible. Hence, $x\nsucc x$ which means that $\succ$ is not reflexive.