# Classification of relations

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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 $a\geq b$ 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 $a\geq b$ is of the same age or older Up a level : Algebra and Arithmetic
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