Is the linear order relation asymmetric and transitive?

Question

Mathematics

The definition states that a linear order relation is a partial order relation and either xPy or yPx.
But because "xPy or yPx" is the definition of an asymmetric order, it does not allow the case x = y.
So the linear order relation is asymmetric and transitive, but not reflexive?

Answer 1

the order relation can be strict or non-strict, and its properties depend on it.

Answer 2

The linear order is characterized by the fact that for it any pair of elements is comparable.
For example: on the set of natural numbers N, the usual relation <= is a linear order (for any pair of natural numbers m, n, at least one of the conditions takes place: m<=n or n<=m). Now let's take the set-power of the set {1, 2} (the set of all subsets of the given set), with the inclusion relation. This order is not linear: {1} is not a subset of {2}, {2} is not a subset of {1}.