Let $\displaystyle I_{a}$ denote the identity relation on a set a

Show that if R is a partial order relation on a then $\displaystyle R\backslash I_{a}$ is a strict partial order relation on a

Show that if S is a strict partial order relation on a then $\displaystyle S \cup I_{a}$ is a partial order relation on a

I'm pretty sure I have these down I just want to make sure

For the first one, this one is just straight forward... I mean if you have a partial order relation and then you take out the identity it becomes irreflexive but I'm not sure how to "show" this. Do I just say:

$\displaystyle x \epsilon R \backslash I_{a} $ means that x cannot be of the form $\displaystyle (x,x)$ making $\displaystyle R \backslash I_{a}$ irreflexive and thus a strict partial order?

The second is basicly the same but the opposite way.