Classification of relations

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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	$a\geq b$	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

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Last modified: Oct 29, 2023 @ 20:14