Binary Relation - Examples of Common Binary Relations

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.
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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