Examples of Common Binary Relations
- order relations, including strict orders:
- greater than
- greater than or equal to
- less than
- less than or equal to
- divides (evenly)
- is a subset of
- equivalence relations:
- equality
- is parallel to (for affine spaces)
- is in bijection with
- isomorphy
- dependency relation, a finite, symmetric, reflexive relation.
- independency relation, a symmetric, irreflexive relation which is the complement of some dependency relation.
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Binary relations by property reflexive symmetric transitive symbol example directed graph → undirected graph No Yes tournament No No pecking order dependency Yes Yes weak order Yes ≤ preorder Yes Yes ≤ preference partial order Yes No Yes ≤ subset partial equivalence Yes Yes equivalence relation Yes Yes Yes ∼, ≅, ≈, ≡ equality strict partial order No No Yes < proper subset
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