Pengguna:Klasüo/bak pasir/templat

Transitif relasi biner

	Simetris	Antisimetris	Terhubung	Paut rapu	Sambungan	Pertemuan	Refleksif	Irefleksif	Asimetris
			Total, Semiterhubung					Anti- refleksif
Relasi ekuivalen	Y	✗	✗	✗	✗	✗	Y	✗	✗
Praurutan (Urutan semu)	✗	✗	✗	✗	✗	✗	Y	✗	✗
Urutan parsial	✗	Y	✗	✗	✗	✗	Y	✗	✗
Praurutan total	✗	✗	Y	✗	✗	✗	Y	✗	✗
Urutan total	✗	Y	Y	✗	✗	✗	Y	✗	✗
Praurutanrapi	✗	✗	Y	Y	✗	✗	Y	✗	✗
Urutan kuasi rapi	✗	✗	✗	Y	✗	✗	Y	✗	✗
Urutan rapi	✗	Y	Y	Y	✗	✗	Y	✗	✗
Kekisi	✗	Y	✗	✗	Y	Y	Y	✗	✗
Semikekisi sambungan	✗	Y	✗	✗	Y	✗	Y	✗	✗
Semikekisi pertemuan	✗	Y	✗	✗	✗	Y	Y	✗	✗
Strict partial order	✗	✗	✗	✗	✗	✗	✗	Y	Y
Strict weak order	✗	✗	✗	✗	✗	✗	✗	Y	Y
Strict total order	✗	✗	Y	✗	✗	✗	✗	Y	Y
	Symmetric	Antisymmetric	Connected	Well-founded	Has joins	Has meets	Reflexive	Irreflexive	Asymmetric
Definitions, for all $a,b$ and $S\neq \varnothing$ :	${\begin{aligned}&aRb\\\Rightarrow {}&bRa\end{aligned}}$	${\begin{aligned}aRb{\text{ and }}&bRa\\\Rightarrow a={}&b\end{aligned}}$	${\begin{aligned}a\neq {}&b\Rightarrow \\aRb{\text{ or }}&bRa\end{aligned}}$	${\begin{aligned}\min S\\{\text{exists}}\end{aligned}}$	${\begin{aligned}a\vee b\\{\text{exists}}\end{aligned}}$	${\begin{aligned}a\wedge b\\{\text{exists}}\end{aligned}}$	$aRa$	${\text{not }}aRa$	${\begin{aligned}aRb\Rightarrow \\{\text{not }}bRa\end{aligned}}$

indicates that the column's property is required by the definition of the row's term (at the very left). For example, the definition of an equivalence relation requires it to be symmetric. All definitions tacitly require the homogeneous relation

R

be transitive: for all

a,b,c,

if

aRb

and

bRc

then

aRc,

and there are additional properties that a homogeneous relation may satisfy.