How do i show that the strict preference (>) ordering is not reflexive. I've tried to prove this by asymmetry but I am not sure this is the way to do it. Any help? Thank You.
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.