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- Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Transitive relation 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 a to c. Every partial order and every equivalence relation is transitive.en.wikipedia.org/wiki/Transitive_relationIn logic and mathematics, transitivity is a property of a binary relation. It is a prerequisite of a equivalence relation and of a partial order.simple.wikipedia.org/wiki/Transitivity_(mathematics)
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See all on WikipediaTransitive relation - Wikipedia
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 a to c. Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c then a … See more
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, … See more• Preorder – a reflexive and transitive relation
• Partial order – an antisymmetric preorder
• Total preorder – a connected (formerly called total) preorder See moreA relation R is called intransitive if it is not transitive, that is, if xRy and yRz, but not xRz, for some x, y, z. In contrast, a relation R is called See more
• Transitive reduction
• Intransitive dice
• Rational choice theory
• Hypothetical syllogism — transitivity of the material conditional See more
Let R be a binary relation on set X. The transitive extension of R, denoted R1, is the smallest binary relation on X such that R1 contains R, and if (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R1. For example, suppose X is a set of towns, some of which are … See more
Wikipedia text under CC-BY-SA license Relation (mathematics) - Wikipedia
Some important properties that a relation R over a set X may have are:
Reflexive for all x ∈ X, xRx. For example, ≥ is a reflexive relation but > is not.
Irreflexive (or strict) for all x ∈ X, not xRx. For example, > is an irreflexive relation, but ≥ is not.
The previous 2 alternatives are not exhaustive; e.g., the red relation y = x give…Wikipedia · Text under CC-BY-SA license- Estimated Reading Time: 5 mins
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Transitivity (mathematics) - Simple English Wikipedia, the free ...
In logic and mathematics, transitivity is a property of a binary relation. It is a prerequisite of an equivalence relation and of a partial order. In general, given a set with a relation, the relation is …
- Estimated Reading Time: 1 min
Equivalence relation - Wikipedia
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 …
Transitive Relations: Definition, Properties, and …
Aug 8, 2024 · Explore the concept of transitive relations, an essential element in mathematics and logic. Learn what transitive relations are, their properties, and see real-life examples to grasp the concept better. Dive into the world of …
Transitive relation | Math Wiki - Fandom
A binary relation R over a set X is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c. In mathematical syntax: …
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Definition:Transitive Relation - ProofWiki
$\RR$ is a transitive relation if and only if: $\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$ that is: $\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} …
Transitive Relations - Definition, Examples, Properties - Cuemath
Transitive relations are binary relations in set theory that are defined on a set A such that if a is related to b and b is related to c, then element a must be related to element c, for a, b, c in set …
Transitive relation - Wikipedia
In mathematics, a binary relation R over a set X is transitive if whenever an element a is related to an element b and b is related to an element c then a is also related to c. Transitivity (or …
Transitive Relations - Definition, Properties, Examples …
What Are Transitive Relations? A relation is said to be a transitive relation, if “a is related to b” and “b is related to c” implies that “a is related to c.”
Transitive closure - Wikipedia
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 sets, "smallest" can be taken …
Transitive Property (Definition and Examples) - BYJU'S
In Mathematics, a transitive relation is defined as a homogeneous relation R over the set A, where the set contains the elements such as x, y and z, such that R relates x to y and y to z, then R …
elementary set theory - What does a transitive set exactly imply ...
Mar 21, 2017 · Transitive set is related to transitivity of the membership (∈ ∈) relation (that, of course, is a relation "from outside" on the universe of sets). A set X X is transitive means that …
Transitive Relation/Examples - ProofWiki
Let $\sim$ be the relation on $P$ defined as: $\forall \tuple {x, y} \in P \times P: x \sim y \iff \text { $x$ is an ancestor of $y$}$ Then $\sim$ is a transitive relation .
Transitive Relation Definition & Examples - Quickonomics
Sep 8, 2024 · Transitive relations are crucial in various mathematical, computational, and logical contexts. Their importance can be observed in the following areas: Equivalence Relations: A …
Transitivity - Wikipedia
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 …
Transitive Relation - (Discrete Mathematics) - Fiveable
Transitive relations can be represented in directed graphs where arrows indicate the relations between elements, helping visualize their connections. The transitive property can be applied …
Transitive relation - Encyclopedia of Mathematics
Nov 17, 2023 · A relation $R$ on a set $A$ is called transitive if, for any $a,b,c\in A$, the conditions $aRb$ and $bRc$ imply $aRc$: equivalently if the composition $R \circ R \subseteq …
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