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, 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...

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

Antitransitivity is a stronger property which describes a relation where, for any three values, the transitivity condition never holds. Some authors use the term...

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...

transitive dependency is an indirect dependency relationship between software components. This kind of dependency is held by virtue of a transitive relation...

reflexive. An asymmetric relation is necessarily irreflexive. A transitive and irreflexive relation is necessarily asymmetric. left quasi-reflexive if whenever...

{\displaystyle (x,z)} , we define the transitive closure of R {\displaystyle R} on A {\displaystyle A} as the smallest relation on A {\displaystyle A} that contains...

Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. "is equal to" (equality) (whereas "is...

Look up transitivity or transitive in Wiktionary, the free dictionary. Transitivity or transitive may refer to: Transitivity (grammar), a property regarding...

{\displaystyle xRz} . A transitive relation is irreflexive if and only if it is asymmetric. For example, "is ancestor of" is a transitive relation, while "is parent...

quasitransitivity is a weakened version of transitivity that is used in social choice theory and microeconomics. Informally, a relation is quasitransitive if it is symmetric...

partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two...

is also necessary) R {\displaystyle R} is irreflexive and transitive. A transitive relation is asymmetric if and only if it is irreflexive: if a R b {\displaystyle...

transitive closure of the membership relation, since the union of a set can be expressed in terms of the relative product of the membership relation with...

this relation; two elements x and y are equivalent if and only if their orbits are the same, that is, G⋅x = G⋅y. The group action is transitive if and...

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

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

of relations by inclusion. If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, connected, trichotomous, a partial...

Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is...

types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes...

consequence of equivalence is that thermal equilibrium is described as a transitive relation:: 56  If A is in thermal equilibrium with B and if B is in thermal...

R)\to X(T)\times X(T)} is an equivalence relation; that is, a reflexive, symmetric and transitive relation. The basic case in practice is when C is the...

more red than Y. The relation ≥ is the disjoint union of the symmetric relation ≈ and the transitive relation >. Using the transitivity of >, the knowledge...

also co-transitive if it is symmetric, left or right Euclidean, transitive, or quasitransitive. If incomparability w.r.t. R is a transitive relation, then...

in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders...

the issue is that interfertility (ability to interbreed) is not a transitive relation; if A breeds with B, and B breeds with C, it does not mean that A...

comparisons, specifically in scenarios where transitivity is expected, however, empirical observations of the binary relation is probabilistic. For example, players'...

A social relation is the fundamental unit of analysis within the social sciences, and describes any voluntary or involuntary interpersonal relationship...