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**Classification of binary Relations**

Binary relations can be classified in many ways. Some is described in the list below. In the examples *a* and *b* are, say, real numbers, when using mathematical symbols.

Type of relation |
Condition |
Description |
Example |
example |

reflexive |
aRa for every a |
every element relates to itself | a=b, |
as old as |

antireflexive |
not aRa for any a |
no elements relates to itself | a>b |
is the mother of |

transitive |
aRb and bRc implies aRc |
the relation form “chains” like a>b>c where a>c, a>b |
a>b |
is older than |

cotransitive |
aRb and cRb implies aRc |
if two relates to a third, then they relate to each other | a=b |
lives in the same country as |

symmetric |
aRb implies bRa |
if a relates to b then b relates to a |
a=b |
is a relative to |

antisymmetric |
aRb and bRa implies a=b |
if a and b relates to each other then they are the same |
has the same passport as | |

asymmetric |
aRb implies not bRa, |
if a relates to b then b does not relate to a |
a>b | is the older brother of |

total |
aRb or bRa | every pair of elements relates to each other in one way or the other | is of the same age or older |

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