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Home > Transitive relation

In notation, this is:

For example, "is greater than" and "is equal to" are transitive relations: if a = b and b = c, then a = c.

On the other hand, "is the mother of" is not a transitive relation, because if Alice is the mother of Brenda, and Brenda is the mother of Claire, then Alice is not the mother of Claire.

Examples of transitive relations include:

• "is equal to" ( equality)
• "is a subset of" (set inclusion)
• "is less than" and "is less than or equal to" ( inequality)
• "divides" ( divisibility)

A transitive relation that is also reflexive is a preorder. A preorder that is antisymmetric is a partial order. A preorder that is symmetric, is an equivalence relation.

See also transitive closure, Intransitivity

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Topics: Transitive Relation Mother Related Set Preorder Equal Alice...

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Transitive verbIn grammar, a transitive verb is a verb that takes both a subject and an object. Some examples of sentences with transitive verbs: I eat food. Mary sees John. You lifted the bag. For examples of other types of verb, see intransitive verb and ditransitive Transitive relationIn mathematics, a binary relation R over a set X is transitive if it holds for all a b and c in X that if a is related to b and b is related to c then a is related to c''. In notation, this is: : For example, "is greater than" and "is equal to" are transi Transitive closureIn mathematics, the transitive closure of a binary relation R on a set X is the smallest transitive relation on X that contains R''. For any relation R the transitive closure of R always exits. To see this note that the intersection of any family of trans