सकर्मक संबंध: Difference between revisions

सकर्मक संबंध
Type	द्विआधारी संबंध
Field	प्राथमिक बीजगणित
Statement	एक सम्बन्ध on a set यदि सभी तत्वों के लिए यह सकर्मक है , , in , जब भी relates to and to , then भी संबंधित है to .
Symbolic statement

Latest revision as of 17:14, 13 September 2023

गणित में, समुच्चय पर संबंध $R$ समुच्चय पर $X$ सकर्मक है यदि, सभी तत्वों के लिए $a$ , $b$ , $c$ में $X$ , जब भी $R$ संबंधित $a$ को $b$ और $b$ को $c$ , तब $R$ संबंध $a$ को $c$ भी रखता है प्रत्येक आंशिक क्रम के साथ-साथ प्रत्येक तुल्यता संबंध को सकर्मक होना चाहिए।

परिभाषा

Transitive binary relations

	Symmetric	Antisymmetric	Connected	Well-founded	Has joins	Has meets	Reflexive	Irreflexive	Asymmetric
			Total, Semiconnex					Anti- reflexive
Equivalence relation	Y	✗	✗	✗	✗	✗	Y	✗	✗
Preorder (Quasiorder)	✗	✗	✗	✗	✗	✗	Y	✗	✗
Partial order	✗	Y	✗	✗	✗	✗	Y	✗	✗
Total preorder	✗	✗	Y	✗	✗	✗	Y	✗	✗
Total order	✗	Y	Y	✗	✗	✗	Y	✗	✗
Prewellordering	✗	✗	Y	Y	✗	✗	Y	✗	✗
Well-quasi-ordering	✗	✗	✗	Y	✗	✗	Y	✗	✗
Well-ordering	✗	Y	Y	Y	✗	✗	Y	✗	✗
Lattice	✗	Y	✗	✗	Y	Y	Y	✗	✗
Join-semilattice	✗	Y	✗	✗	Y	✗	Y	✗	✗
Meet-semilattice	✗	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 $S\neq \varnothing :$	${\begin{aligned}&aRb\\\Rightarrow {}&bRa\end{aligned}}$	${\begin{aligned}aRb{\text{ and }}&bRa\\\Rightarrow a={}&b\end{aligned}}$	${\begin{aligned}a\neq {}&b\Rightarrow \\aRb{\text{ or }}&bRa\end{aligned}}$	${\begin{aligned}\min S\\{\text{exists}}\end{aligned}}$	${\begin{aligned}a\vee b\\{\text{exists}}\end{aligned}}$	${\begin{aligned}a\wedge b\\{\text{exists}}\end{aligned}}$	$aRa$

@@ Line 117: / Line 117: @@
 * {{springer|title=Transitivity|id=p/t093810}}
 * [http://www.cut-the-knot.org/triangle/remarkable.shtml Transitivity in Action] at [[cut-the-knot]]
-[[Category:द्विआधारी संबंध]][[श्रेणी: प्रारंभिक बीजगणित]][[श्रेणी:सकर्मक संबंध|सकर्मक संबंध]]
+[[Category:All articles with bare URLs for citations]]
-[[Category: Machine Translated Page]]
+[[Category:Articles with PDF format bare URLs for citations]]
+[[Category:Articles with bare URLs for citations from March 2022]]
+[[Category:Articles with hatnote templates targeting a nonexistent page]]
+[[Category:CS1 English-language sources (en)]]
 [[Category:Created On 05/01/2023]]
-[[Category:Vigyan Ready]]
+[[Category:Lua-based templates]]
+[[Category:Machine Translated Page]]
+[[Category:Mathematics sidebar templates]]
+[[Category:Pages with script errors]]
+[[Category:Short description with empty Wikidata description]]
+[[Category:Templates Vigyan Ready]]
+[[Category:Templates that add a tracking category]]
+[[Category:Templates that generate short descriptions]]
+[[Category:Templates using TemplateData]]
+[[Category:द्विआधारी संबंध]]

Anonymous

Search

सकर्मक संबंध: Difference between revisions

Namespaces

More

Page actions

Latest revision as of 17:14, 13 September 2023

Contents

परिभाषा