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Transitivity (mathematics) Facts for Kids. Kiddle Encyclopedia.Transitivity (mathematics) facts for kids
In logic and mathematics, transitivity is a property of a binary relation. It is a prerequisite of a equivalence relation and of a partial order.
Definition and examples
In general, given a set with a relation, the relation is transitive if whenever a is related to b and b is related to c, then a is related to c. For example:
- Size is transitive: if A>B and B>C, then A>C.
- Subsets are transitive: if A is a subset of B and B is a subset of C, then A is a subset of C.
- Height is transitive: if Sidney is taller than Casey, and Casey is taller than Jordan, then Sidney is taller than Jordan.
- Rock, paper, scissors is not transitive: rock beats scissors, and scissors beats paper, but rock doesn't beat paper. This is called an intransitive relation.
Given a relation , the smallest transitive relation containing
is called the transitive closure of
, and is written as
.
Related pages
- Symmetric relation
See also
In Spanish: Relación transitiva para niños