Total orderings

Question

First they need to be in partiel ordning, which only E, H and I fulfill. then every two elements in the set need to be comparable, the relation is then called a total ordering, but how do I figure out if there are comparable?

Answer 1

A total order is reflexive, anti-symmetric, transitive, and has the property that every pair of elements is comparable.

Let's look at $E$, $H$, and $I$; the partial orders. Since $E$ has no relation between $a$ and $c$, it cannot be a total order.

Both $H$ and $I$ are total orders, $H$ stating $a < b < c$ and $I$ stating $a < c < b$.