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Transitive Relations
Transitivity or transitive may refer to: Grammar * Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object * Transitive verb, a verb which takes an object * Transitive case, a grammatical case to mark arguments of a transitive verb Logic and mathematics * Transitive group action * Transitive relation, a binary relation in which if ''A'' is related to ''B'' and ''B'' is related to ''C'', then ''A'' is related to ''C'' * Syllogism, a related notion in propositional logic * Intransitivity, properties of binary relations in mathematics * Arc-transitive graph, a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices * Edge-transitive graph, a graph whose automorphism group acts transitively upon its edges * Vertex-transitive graph, a graph whose automorphism group acts transitively upon its vertices * Transitive set In set theory, a branch of mathematics, a set A is called transitive if either of the foll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitivity (grammar)
Transitivity is a linguistics property that relates to whether a verb, participle, or gerund denotes a Object (grammar), transitive object. It is closely related to valency (linguistics), valency, which considers other argument (linguistics), arguments in addition to transitive objects. English grammar makes a binary distinction between intransitive verbs (e.g. ''arrive'', ''belong'', or ''die'', which do not denote a transitive object) and transitive verbs (e.g., ''announce'', ''bring'', or ''complete'', which must denote a transitive object). Many languages, including English, have ditransitive verbs that denote two objects, and some verbs may be ambitransitive verb, ambitransitive in a manner that is either transitive (e.g., "I ''read'' the book" or "We ''won'' the game") or intransitive (e.g., "I ''read'' until bedtime" or "We ''won''") depending on the given context. History The notion of transitivity, as well as other notions that today are the basics of linguistics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Verb
A transitive verb is a verb that entails one or more transitive objects, for example, 'enjoys' in ''Amadeus enjoys music''. This contrasts with intransitive verbs, which do not entail transitive objects, for example, 'arose' in ''Beatrice arose''. Transitivity is traditionally thought of as a global property of a clause, by which activity is transferred from an agent to a patient. Transitive verbs can be classified by the number of objects they require. Verbs that entail only two arguments, a subject and a single direct object, are monotransitive. Verbs that entail two objects, a direct object and an indirect object, are '' ditransitive'', or less commonly ''bitransitive''. An example of a ditransitive verb in English is the verb ''to give'', which may feature a subject, an indirect object, and a direct object: ''John gave Mary the book''. Verbs that take three objects are ''tritransitive''. In English a tritransitive verb features an indirect object, a direct object, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Case
In linguistic typology, transitive alignment is a type of morphosyntactic alignment used in a small number of languages in which a single grammatical case is used to mark both arguments of a transitive verb, but not with the single argument of an intransitive verb. Such a situation, which is quite rare among the world's languages, has also been called a ''double- oblique'' clause structure. Rushani, an Iranian dialect, has this alignment in the past tense. That is, in the past tense (or perhaps perfective aspect), the agent and object of a transitive verb are marked with the same case ending, while the subject of an intransitive verb is not marked. In the present tense, the object of the transitive verb is marked, the other two roles are not – that is, a typical nominative–accusative alignment.J.R. Payne, 'Language Universals and Language Types', in Collinge, ed. 1990. ''An Encyclopedia of Language''. Routledge. From Payne, 1980. According to Payne, it's clear what hap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Group Action
In mathematics, a group action of a group G on a set S is a group homomorphism from G to some group (under function composition) of functions from S to itself. It is said that G acts on S. Many sets of transformations form a group under function composition; for example, the rotations around a point in the plane. It is often useful to consider the group as an abstract group, and to say that one has a group action of the abstract group that consists of performing the transformations of the group of transformations. The reason for distinguishing the group from the transformations is that, generally, a group of transformations of a structure acts also on various related structures; for example, the above rotation group also acts on triangles by transforming triangles into triangles. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transitive Relation
In mathematics, a binary relation on a set (mathematics), set is transitive if, for all elements , , in , whenever relates to and to , then also relates to . Every partial order and every equivalence relation is transitive. For example, less than and equality (mathematics), equality among real numbers are both transitive: If and then ; and if and then . Definition A homogeneous relation on the set is a ''transitive relation'' if, :for all , if and , then . Or in terms of first-order logic: :\forall a,b,c \in X: (aRb \wedge bRc) \Rightarrow aRc, where is the infix notation for . Examples As a non-mathematical example, the relation "is an ancestor of" is transitive. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy is also an ancestor of Carrie. On the other hand, "is the birth mother of" is not a transitive relation, because if Alice is the birth mother of Brenda, and Brenda is the birth mother of Claire, then it does ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book '' Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intransitivity
In mathematics, intransitivity (sometimes called nontransitivity) is a property of binary relations that are not transitive relations. That is, we can find three values a, b, and c where the transitive condition does not hold. Antitransitivity is a Mathematical jargon#stronger, stronger property which describes a relation where, for any three values, the transitivity condition never holds. Some authors use the term to refer to antitransitivity. Intransitivity A relation is transitive if, whenever it relates some A to some B, and that B to some C, it also relates that A to that C. A relation is if it is not transitive. Assuming the relation is named R, it is intransitive if: \lnot\left(\forall a, b, c: a R b \land b R c \implies a R c\right). This statement is equivalent to \exists a,b,c : a R b \land b R c \land \lnot(a R c). For example, the inequality relation, \neq, is intransitive. This can be demonstrated by replacing R with \neq and choosing a=1, b=2, and c=1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arc-transitive Graph
In the mathematical field of graph theory, a graph is symmetric or arc-transitive if, given any two ordered pairs of adjacent vertices (u_1,v_1) and (u_2,v_2) of , there is an automorphism :f : V(G) \rightarrow V(G) such that :f(u_1) = u_2 and f(v_1) = v_2. In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called -transitive or flag-transitive. By definition (ignoring and ), a symmetric graph without isolated vertices must also be vertex-transitive. Since the definition above maps one edge to another, a symmetric graph must also be edge-transitive. However, an edge-transitive graph need not be symmetric, since might map to , but not to . Star graphs are a simple example of being edge-transitive without being vertex-transitive or symmetric. As a further example, semi-symmetric graphs are edge-transitive and regula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edge-transitive Graph
In the mathematical field of graph theory, an edge-transitive graph is a graph such that, given any two edges and of , there is an automorphism of that maps to . In other words, a graph is edge-transitive if its automorphism group acts transitively on its edges. Examples and properties The number of connected simple edge-transitive graphs on n vertices is 1, 1, 2, 3, 4, 6, 5, 8, 9, 13, 7, 19, 10, 16, 25, 26, 12, 28 ... Edge-transitive graphs include all symmetric graphs, such as the vertices and edges of the cube. Symmetric graphs are also vertex-transitive (if they are connected), but in general edge-transitive graphs need not be vertex-transitive. Every connected edge-transitive graph that is not vertex-transitive must be bipartite, (and hence can be colored with only two colors), and either semi-symmetric or biregular.. Examples of edge but not vertex transitive graphs include the complete bipartite graph In the mathematical field of graph theory, a comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex-transitive Graph
In the mathematics, mathematical field of graph theory, an Graph automorphism, automorphism is a permutation of the Vertex (graph theory), vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is a vertex-transitive graph if, given any two vertices and of , there is an automorphism such that :f(v_1) = v_2.\ In other words, a graph is vertex-transitive if its automorphism group Group action (mathematics), acts Group_action#Remarkable properties of actions, transitively on its vertices.. A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical. Every symmetric graph without isolated vertex, isolated vertices is vertex-transitive, and every vertex-transitive graph is Regular graph, regular. However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
