I have a question here that asks:
Determine whether each of the following relations is a partial order and state whether each partial order is a total order.
i) (R, partial order symbol), where a is a partial order of b means aČ is less than or equal to bČ
ii) (N x N, partial order symbol), where (a,b) is a partial order of (c,d) if and only if a is less than or equal to c and b is greater than or equal to d.
I am having a fair amount of trouble trying to wrap my head around partial orders, so any help would be greatly appreciated. Thanks.