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Topic: Transitive relation

	Transitive Closure on the Instruction Systolic Array
		Furthermore, a generalization of the transitive closure algorithm is implemented to solve other path problems, such as the shortest path problem.
		The transitive closure problem may be generalized to the algebraic path problem.
		The problem of computing the transitive closure of a graph may be viewed as a special case of the algebraic path problem.
	www.iti.fh-flensburg.de /lang/papers/trans/transcl.htm (3699 words)

	Transitive relation - Wikipedia, the free encyclopedia
		In mathematics, a binary relation R over a set X is transitive if it holds for all a, b, and c in X, that if a is related to b and b is related to c, then a is related to c.
		Unlike other relation properties, it is not possible to find a general formula that counts the number of transitive relations on a finite set.
		equivalence relation - a relation that is a preorder and symmetric.
	en.wikipedia.org /wiki/Transitive_relation (254 words)

	Equivalence relation - Wikipedia, the free encyclopedia
		Green's relations are five equivalence relations on the elements of a semigroup.
		The relation "is a sibling of" on the set of all human beings is not an equivalence relation, and it is worthwhile example to consider.
		The relation is "almost transitive", insofar as whenever A is a sibling of B, and B is a sibling of C, and A
	en.wikipedia.org /wiki/Equivalence_relation (1350 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-19)
		Transitive Relation Again the definition says if (a,b) and (b,c) is present then (a,c) has to be present to make the relation transitive.
		Transitivity ------------ A relation R on a set A is transitive if: "For all x,y,z in A, ((x,y) in R) AND ((y,z) in R)) -> (x,z) in R" Note that x,y,z need not be different.
		Consider now the relation: R = {(1,2),(2,1)} In this case, if we let x = 1, y = 2, z = 1, we see that (x,y) = (1,2) is in R (y,z) = (2,1) is in R (x,z) = (1,1) is not in R and this shows that the relation is not transitive.
	mathforum.org /library/drmath/view/63001.html (1421 words)

	Welcome LP
		For example, "descendent of" is a typical transitive relation: if "Marry" is a decscendent of "Paul" and "Paul" is a descendent of "Jim" than clearly "Marry" is a descendent of "Jim".
		By the same token, many famous relations are not transitive: eg in general "mother of" is not a transitive relation: { "Lynn" is the mother "Marry" and "Marry" is a the mother of "Paul" } does not entail that "Lynn" is the mother of "Paul".
		Since we deal only with relations on finite sets, it is convenient to represent the relations as boolean matrices where the pairs (a,b) in a relation are represented by 1's in the respective (row,column) pairs.
	www.tutor.ms.unimelb.edu.au /transitivity/transitivity.html (414 words)

	Binary Relation
		With the definition of a relation explicitly stated, one is able to not only construct examples, but also define an algebra (used vaguely, not as the mathematical concept in the branch of mathematics called algebra) on relations.
		Another interesting topic in the study of relation is the study of relation on a set X. In this case, both the domain and range of the relation are subsets of X. On these relations, mathematicians use a few adjectives to describe the different elementary types of relation on a given set.
		The power invested in relation comes from two sources: the set structure of relation and its interpretation as a relationship (in the quotidian parlance) from an element in the first set to an element in the second set.
	www.iscid.org /encyclopedia/Binary_Relation (2105 words)

	[No title]
		Explanation: _____________________________________________________ The relation “is a sister or brother of” is / is not a symmetric relation.
		Explanation: _____________________________________________________ The relation “is married to” is / is not a symmetric relation.
		Explanation: _____________________________________________________ The relation “is in” is / is not a transitive relation.
	www.weizmann.ac.il /usersfiles/zemed/upload/(FILE)1138777321.doc (3073 words)

	241 Week 4
		The relation is not transitive, because (2,1) and (1,3) exist, but (2,3) does not.
		To determine whether the relation on the given directed graph is a partial order, we will map out the coordinates and compare the ordered pairs of the relation for its properties.
		This relation is not transitive, however, since (c,d) and (d,b) exist, but (c,b) does not.
	www2.hawaii.edu /~kumasaki/Kumasaki_Evan.Week4.htm (2470 words)

	plope - Descriptions of Relation Terminology
		A relation R is non-transitive iff it is neither transitive nor intransitive.
		A relation R is non-symmetric iff it is neither symmetric nor asymmetric.
		A relation R is non-reflexive iff it is neither reflexive nor irreflexive.
	www.plope.com /Members/chrism/relationship_terminology (471 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-19)
		Date: 11/10/98 at 11:30:27 From: Mike Subject: Discrete math Suppose R is a symmetric and transitive relation on A. Suppose that for each a in A there is b in A such that (a,b) and is in R. Show: R is an equivalence relation.
		To show that a relation R is an equivalence relation, we need to prove that it has three properties.
		Try finishing the proof using the facts that R is transitive and for each a in A, (a,b) and (b,a) are in R. Once you have finished the first proof, the second two are very similar.
	mathforum.org /library/drmath/view/54256.html (1126 words)

	Order Relation
		Example 4: The relation {< 1, 1 >, < 1, 2 >, < 1, 3 >, < 2, 3>, < 3, 3 > } on the set of integers {1, 2, 3} is neither reflexive nor irreflexive.
		Example 5: The relation = on the set of integers {1, 2, 3} is {<1, 1>, <2, 2> <3, 3> } and it is symmetric.
		(b) is neither reflexive nor irreflexive, and it is antisymmetric, symmetric and transitive.
	www.cs.odu.edu /~toida/nerzic/content/relation/property/property.html (550 words)

	Notation
		The concept of binary relation itself is too general for practical use.
		Transitive relation: A relation R is transitive when aRb and bRc imply aRc, i.e.
		Equivalence relation: A relation R defined on a set V is an equivalent relation when it is
	www.unesco.org /webworld/idams/advguide/Chapt2_2_2.htm (386 words)

	Lecture 23--shortest path algorithms; transitive closure. 11/19/97.
		Now clearly this relation may not be transitive, i.e., there may be vertices v,w,z where there is an edge from v to w and an edge from w to z but no edge from v to z.
		In fact T is the transitive closure of the relation relating vertices v,w if there is an edge from v to w, i.e., T is a transitive relation, T contains all pairs of vertices joined by an edge, and T is the smallest transitive relation containing the edge pairs.
		Floyd-Warshall algorithm for transitive closure of a graph G. Input: A, the adjacency matrix for G. Output: R, the adjacency matrix for the transitive closure of G.
	www.ececs.uc.edu /~cpurdy/lec332_7.html (1050 words)

	Computers and Vision Lecture - 29 August 1994 (Site not responding. Last check: 2007-10-19)
		It is often helpful to envision a relation as a directed graph with nodes corresponding to the elements of A and arcs corresponding to the pairs in R.
		One forms the transitive closure of a non-transitive relation by adding all those pairs and only those pairs that are necessary to cause the relation to be transitive.
		The reflexive-transitive closure of a relation is the result of forming the transitive closure of the reflexive closure of the relation.
	www.cise.ufl.edu /~jnw/VisionCourse/Lectures/94.08.29.html (465 words)

	No Title (Site not responding. Last check: 2007-10-19)
		The parent of relations, ``x is a parent of y'', is a binary relation between pairs of people.
		If there is a path from a to c in a transitive relation, there must be a single arc from a to c.
		This relation is reflexive, symmetric, and transitive, and hence is an equivalence relation.
	www.cs.sunysb.edu /~cse113/ref/lecture22/lecture22.html (978 words)

	2 Building fuzzy transitive relations
		To be more concrete, in order to apply the transitive closure method to construct a similarity relation and, in general, a fuzzy T-transitive relation, a reflexive and symmetric fuzzy relation has to be used as a starting point.
		In others words, an index of similarity relating each couple of elements in the sample set has to be given: each two elements should be matched, in some way, and then the method is applied to obtain either a similarity or dissimilarity measure.
		It is worth noting that reflexive, symmetric and Z-transitive fuzzy relations are simply those reflexive and symmetric relations for which the 1-level set is a classical equivalence relation.
	dmi.uib.es /people/valverde/gran1/node2.html (1011 words)

	Glossary: T
		A relationship can be transitive, which simply means that two entities from a set are related if they are both related to a common, mediating entity from the same set.
		A R B (i.e., A is related to B)
		transitive, as are the "proper subtype-relation" and "proper supertype-relation".
	www.huminf.aau.dk /cg/Glossary/T.html (667 words)

	Report from markers on grading of homework 9, question 1 (Site not responding. Last check: 2007-10-19)
		Let R be some binary relation in A. Show R is a subset of X^Y. R is a subset of X and R is a subset of Y due to property (ii).
		Therefore, as all relations in Q are transitive, R' is transitive.
		Let S be a transitive binary relation where R is a subset of S. Therefore, S is an element of Q. Therefore, R' = S ^(Other sets in Q).
	www.cs.ubc.ca /~condon/cpsc220/homeworks/h9q1.html (260 words)

	transitive - Wiktionary
		For all symbols are fluxional; all language is vehicular and transitive, and is good, as ferries and horses are, for conveyance, not as farms and houses are, for homestead.
		By far the greater part of the transitive or derivative applications of words depend on casual and unaccountable caprices of the feelings or the fancy.
		"Is an ancestor of" is a transitive relation.
	en.wiktionary.org /wiki/transitive (160 words)

	Welcome LP
		For example, "descendent of" is a typical transitive relation: if "Marry" is a descendent of "Paul" and "Paul" is a descendent of "Jim" than clearly "Marry" is a descendent of "Jim".
		Therefore we are interested only in the transitive closure of relations that are not themselves transitive.
		The module will enable you to compute the transitive closure of relations represented by box diagrams.
	www.ifors.ms.unimelb.edu.au /tutorial/transitive (724 words)

	M3000 Homework #13
		and we have that n R p, i.e., the relation is transitive.
		Therefore, (x,y) R (u,v) and the relation is transitive.
		Since 3 does not divide 2, 1 S 1 is not true, showing that the relation is not reflexive.
	www-math.cudenver.edu /~wcherowi/courses/m3000/abhw13.html (1404 words)

	Section 4.5 Review
		The term 'relation' is used to describe a relationship between one thing and another.
		The notation used to indicate a relation between 2 elements a and b is denoted by a
		Suppose that a relation is defined as a + 1 = b.
	pandora.compsci.ualr.edu /srini/DM/chapters/review4.5.html (1078 words)

	Transitive relation - ASP Free
		Discuss Transitive relation in the Visual Basic Programming forum on ASP Free.
		Transitive is if there was (1,2) AND (2,3) Then there should be (1,3) in the entered set.
		These are some ideas i thought but I couldn't complete it, also I thought about comparing array2 and string2 (before removing braces) and do some operations on them such as Instr etc...
	forums.aspfree.com /visual-basic-programming-38/transitive-relation-167412.html?goto=lastpost (871 words)

	Detecting transitive behavior in reversible one dimensional cellular automata
		In this transition relation, the indices are sequences
		As in the connectivity relation defined in Table 1, we can do the transitive closure of the transition relation.
		In this way, we have defined simple matrix methods that using the properties of block permutations and transitive closures detect periodical and transitive behavior.
	delta.cs.cinvestav.mx /~mcintosh/comun/summer2000/seck/node12.html (490 words)

	No Title
		The parent of relations, ``...is a parent of...'', is a binary relation between pairs of people.
		The universal and identity relations are both equivalence relations.
		What an equivalence relation means is that the elements can be partitioned into equalence classes (or blocks) such that all elements in the same block have the same properties.
	www.cs.sunysb.edu /~skiena/113/lectures/lecture22/lecture22.html (923 words)

	Partial Order Scoring (statistics)
		Note that the commonly used 'equality' relation, (=), defined on the set of real numbers is an equivalence relation.
		In the situation of equality, the comparison is continued using variables of the next priority level.
		This procedure is repeated until the relation is determined at one of the priority levels, or the end of the variable list is reached.
	www.unesco.org /webworld/idams/Doc/ManualHtml/E2poscor.htm (499 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		* binary relation on S is a subset of S X S, call it A * Can be represented by an adjacency matrix, which is an important relation in itself.
		* A relation is transitive iff for all x, y, z in S xAy, yAz implies xAz.
		* Reachability relation (there is a path from v to w) is an example of a transitive closure relation of a transitive relation.
	www.unf.edu /public/cot4400/ree/Notes/ch8.notes (571 words)

	Groups In Which Commutativity Is A Transitive Relation (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		Groups In Which Commutativity Is A Transitive Relation
		We investigate the structure of groups in which commutativity is a transitive relation on non-identity elements (CT -groups).
		A detailed study of locally finite, polycyclic, and torsion-free solvable CT -groups is carried out.
	citeseer.ist.psu.edu /1355.html (388 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		A least element but A greatest element but no greatest element no least element¡(WZª ÎóRO¨Summary¨,A binary relation on a set S is a subset of SxS.
		Binary relations can have properties of reflexivity, symmetry, anti-symmetry, and transitivity.
		A equivalence relation on a set S defines a partition of S. Partial orders.
	www.cs.uic.edu /~i201/cs201-relation-function.ppt (471 words)

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