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For example, the Spanish reflexive construct "se hundió el barco" ("the boat sank") has no reflexive equivalent in some Slavic languages (which use an intransitive equivalent of sink), though for example Czech and Slovak do use a reflexive verb: "loď se potopila"/"loď sa potopila". Reflexive verbs can have a variety of uses and meanings ...
The relation "≥" between real numbers is reflexive and transitive, but not symmetric. For example, 7 ≥ 5 but not 5 ≥ 7. The relation "has a common factor greater than 1 with" between natural numbers greater than 1, is reflexive and symmetric, but not transitive. For example, the natural numbers 2 and 6 have a common factor greater than 1 ...
A transitive relation is asymmetric if and only if it is irreflexive. [6] A transitive relation need not be reflexive. When it is, it is called a preorder. For example, on set X = {1,2,3}: R = { (1,1), (2,2), (3,3), (1,3), (3,2) } is reflexive, but not transitive, as the pair (1,2) is absent,
An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
An example is the relation being a sibling of: no one is their own sibling. [73] These structural features are used to define further types of relations, like equivalence and strict partial order. An equivalence relation is a relation that is reflexive, symmetric, and transitive, like equality expressed through the symbol "=". [74]
Of particular importance are relations that satisfy certain combinations of properties. A partial order is a relation that is reflexive, antisymmetric, and transitive, [3] an equivalence relation is a relation that is reflexive, symmetric, and transitive, [4] a function is a relation that is right-unique and left-total (see below). [5] [6]
Reflexive. A binary relation R on a set X is reflexive, if x R x holds for every element x in X. Residual. A dual map attached to a residuated mapping. Residuated mapping. A monotone map for which the preimage of a principal down-set is again principal. Equivalently, one component of a Galois connection.
An example in modern English is the verb to arrive. Verbs that can be used in an intransitive or transitive way are called ambitransitive verbs. In English, an example is the verb to eat; the sentences You eat (with an intransitive form) and You eat apples (a transitive form that has apples as the object) are both grammatical.