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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