In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates...

mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in...

mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite...

is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive, symmetric, and transitive, a function...

{\displaystyle (x,z).} A relation is transitive if it is closed under this operation, and the transitive closure of a relation is its closure under this...

ordered as u ≤ v ≤ w. The transitive closure of a DAG is the graph with the most edges that has the same reachability relation as the DAG. It has an edge...

is symmetric and transitive. If the relation is also reflexive, then the relation is an equivalence relation. Formally, a relation R {\displaystyle R}...

reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations. A relation R {\displaystyle R} on the...

antisymmetric, let alone asymmetric. Transitive for all x, y, z ∈ X, if xRy and yRz then xRz. A transitive relation is irreflexive if and only if it is...

reachability relation as D. Equivalently, D and its transitive reduction should have the same transitive closure as each other, and the transitive reduction...