Partial Order Relation help
Let denote the identity relation on a set a
Show that if R is a partial order relation on a then is a strict partial order relation on a
Show that if S is a strict partial order relation on a then 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:
means that x cannot be of the form making irreflexive and thus a strict partial order?
The second is basicly the same but the opposite way.