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nonreflexive relation
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nonreflexive relation

logic
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Quick Summary

In logic, a relation is a set of ordered pairs, triples, or more. A relation can have properties like symmetry, transitivity, and reflexivity.1

  • Symmetrical: If a relation holds between x and y, it also holds between y and x (e.g., "x is parallel to y").1
  • Transitive: If a relation holds between x and y, and between y and z, it also holds between x and z (e.g., "x is greater than y").12
  • Reflexive: A relation always holds between an object and itself (e.g., "x is at least as tall as y").1

A nonreflexive relation is one that is neither reflexive nor irreflexive. This means that for some objects, the relation holds between them and themselves, and for others, it does not. An example is "admires".3

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4 Britannica Sources
  1. relation
  2. formal logic - Classification of dyadic relations
  3. set theory - Cardinality and transfinite numbers
  4. transitive law

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