x R y and y R x implies x = y for all x, y ∈ A. If R is represented as a directed graph (digraph), then whenever there is an edge from x to y with x ≠ y, then there is no edge from y to x.

x R y and y R z implies x R z for all x, y, z ∈ A. If R is represented as a directed graph (digraph), then whenever there are edges from x to y and from y to z, there must also be an edge from x to z.

(x, x) ∉ R for all x ∈ A. If R is represented as a directed graph (digraph), then there are no loop edges from x to x for all x ∈ A.

x R y implies y R x for all x,y ∈ A. If R is represented as a directed graph (digraph), then for each edge from x to y, there is also an edge from y to x for each x,y ∈ A.