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

Read more about this topic:  Binary Relation

Famous quotes containing the words examples of, examples, common and/or relations:

    “It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
    —G.C. (Georg Christoph)

    “Histories are more full of examples of the fidelity of dogs than of friends.”
    —Alexander Pope (1688–1744)

    “So didst thou travel on life’s common way,
    In cheerful godliness; and yet thy heart
    The lowliest duties on herself did lay.”
    —William Wordsworth (1770–1850)

    “Think of the many different relations of form and content. E.g., the many pairs of trousers and what’s in them.”
    —Mason Cooley (b. 1927)