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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 | Examples Reflexive |
---|---|---|---|
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 |
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 | |
asymmetric | aRb implies not bRa | if a relates to b then b does not relate to a | |
total | aRb or bRa | every pair of elements relates to each other in one way or the other |
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