Let us consider R . R is reflexive, transitive, and R is transitive. We introduce R is a quasi order as a synonym of R is quasi-order.
R is reflexive, transitive, R is transitive, antisymmetric, and R is antisymmetric.
We introduce R is a partial order as a synonym of R is partial-order. R is reflexive, transitive, R is transitive, antisymmetric, R is antisymmetric, connected, and R is connected. We introduce R is a linear order as a synonym of R is linear-order. If R is a partial order, then R is a partial order. If R is a linear order, then R is a linear order.