CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16, CBSE Previous Year Question Papers Class 12 Maths, CBSE Previous Year Question Papers Class 10 Maths, ICSE Previous Year Question Papers Class 10, ISC Previous Year Question Papers Class 12 Maths. Reflexive definition is - directed or turned back on itself; also : overtly and usually ironically reflecting conventions of genre or form. This finding resonates well with a previous study showing no evidence of heritability for the ... eye gaze triggers a reflexive attentional orienting may be because it represents a ... political, institutional, religious or other) that a reasonable reader would want to know about in relation to the submitted work. Solution: The relation is not reflexive if a = -2 ∈ R. But |a – a| = 0 which is not less than -2(= a). However, an emphatic pronoun simply emphasizes the action of the subject. [6][7], A binary relation over a set in which every element is related to itself. In the sets theory, a relation is a way of showing a connection or relationship between two sets. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. The given set R is an empty relation. Reflexive-transitive closure: Kaba: 7/9/12 4:06 AM: Hi, The reflexive-transitive closure of a relation R subset V^2 is the intersection of all those relations in V which are reflexive and transitive (at the same time). So for example, when we write , we know that is false, because is false. Reflexive Property – Examples. "Is married to" is not. A relation R is symmetric if the value of every cell (i, j) is same as that cell (j, i). Posted at 04:42h in Uncategorized by 0 Comments. Therefore, the total number of reflexive relations here is 2n(n-1). Of, relating to, or being the pronoun used as the direct object of a reflexive verb, as herself in She dressed herself. In mathematics, a binary relation R over a set X is reflexive if it relates every element of X to itself. is r reflexive irreflexive both or neither explain why. That is, it is equivalent to ~ except for where x~x is true. A binary relation from A to B is a subset of a Cartesian product A x B. R t•Le A x B means R is a set of ordered pairs of the form (a,b) where a A and b B. There are nine relations in math. Examples of irreflexive relations include: The number of reflexive relations on an n-element set is 2n2−n. Be warned. [5], Authors in philosophical logic often use different terminology. Two numbers are only equal to each other if and only if both the numbers are same. A reflexive relation on a nonempty set X can neither be irreflexive, nor asymmetric, nor antitransitive. Equivalence relation Proof . 2 CS 441 Discrete mathematics for CS M. Hauskrecht Binary relation Definition: Let A and B be two sets. Thus, it has a reflexive property and is said to hold reflexivity. Given the usual laws about marriage: If x is married to y then y is married to x. x is not married to x (irreflexive) There are n diagonal values, total possible combination of diagonal values = 2 n There are n 2 – n non-diagonal values. For example, the reflexive closure of (<) is (≤). Reflexive pronouns show that the action of the subject reflects upon the doer. Let R be an equivalence relation on a set A. A reflexive relation is said to have the reflexive property or is meant to possess reflexivity. 2. A relation that is reflexive, antisymmetric, and transitive is called a partial order. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations. Let R be the relation "⊆" defined on THE SET OF ALL SUBSETS OF X. Now, the reflexive relation will be R = {(1, 1), (2, 2), (1, 2), (2, 1)}. [1][2] Formally, this may be written ∀x ∈ X : x R x, or as I ⊆ R where I is the identity relation on X. Two fundamental partial order relations are the “less than or equal” relation on a set of real numbers and the “subset” relation on a set of sets. Q.2: A relation R is defined on the set of all real numbers N by ‘a R b’ if and only if |a-b| ≤ b, for a, b ∈ N. Show that the R is not reflexive relation. Translation memories are created by human, but computer aligned, which might cause mistakes. The statements consisting of these relations show reflexivity. Reflexive words show that the person who does the action is also the person who is affected by it: In the sentence "She prides herself on doing a good job ", " prides " is a reflexive verb and "herself" is a reflexive pronoun. Transposing Relations: From Maybe Functions to Hash Tables. Then I would have better understood that each element in this set is a set. x is married to the same person as y iff (exists z) such that x is married to z and y is married to z. Number of reflexive relations on a set with ‘n’ number of elements is given by; Suppose, a relation has ordered pairs (a,b). So, the set of ordered pairs comprises n2 pairs. For example, the binary relation "the product of x and y is even" is reflexive on the set of even numbers, irreflexive on the set of odd numbers, and neither reflexive nor irreflexive on the set of natural numbers. So, R is a set of ordered pairs of sets. The reflexive reduction, or irreflexive kernel, of a binary relation ~ on a set X is the smallest relation ≆ such that ≆ shares the same reflexive closure as ~. Hence, a number of ordered pairs here will be n2-n pairs. Let us look at an example in Equivalence relation to reach the equivalence relation proof. Formally, this may be written ∀x ∈ X : x R x, or as I ⊆ R where I is the identity relation on X. Table 3 provides the percentage of equivalence, calculated in relation to the Bulgarian reflexive verbs, taken as the basis. Q.3: A relation R on the set A by “x R y if x – y is divisible by 5” for x, y ∈ A. language. Show that R is a reflexive relation on set A. Theorem 2. They come from many sources and are not checked. This means that if a reflexive relation is represented on a digraph, there would have to be a loop at each vertex, as is shown in the following figure. 5 ∙ 3 = 3 ∙ 5. Here are some instances showing the reflexive residential property of equal rights applied. Your email address will not be published. Required fields are marked *. Thus, it makes sense to prove the reflexive property as: Proof: Suppose S is a subset of X. 08 Jan. is r reflexive irreflexive both or neither explain why. Of, relating to, or being a verb having an identical subject and direct object, as dressed in the sentence She dressed herself. Equivalently, it is the union of ~ and the identity relation on X, formally: (≃) = (~) ∪ (=). Not every relation which is not reflexive is irreflexive; it is possible to define relations where some elements are related to themselves but others are not (i.e., neither all nor none are). Reflexive property, for all real numbers x, x = x. Translation memories are created by human, but computer aligned, which might cause mistakes. Therefore, the relation R is not reflexive. Example: 4 = 4 or 4 = 4. The following properties are true for the identity relation (we usually write as ): 1. is {\em reflexive}: for any object , (or ). Showing page 1. In Mathematics of Program Construction (p. 337). … Your email address will not be published. Check if R is a reflexive relation on set A. Q.4: Consider the set A in which a relation R is defined by ‘x R y if and only if x + 3y is divisible by 4, for x, y ∈ A. Grammar a. Now 2x + 3x = 5x, which is divisible by 5. If R is a relation on the set of ordered pairs of natural numbers such that \(\begin{align}\left\{ {\left( {p,q} \right);\left( {r,s} \right)} \right\} \in R,\end{align}\), only if pq = rs.Let us now prove that R is an equivalence relation. It does make sense to distinguish left and right quasi-reflexivity, defined by ∀ x, y ∈ X : x ~ y ⇒ x ~ x[3] and ∀ x, y ∈ X : x ~ y ⇒ y ~ y, respectively. Symmetry, transitivity and reflexivity are the three properties representing equivalence relations. Also, there will be a total of n pairs of (a, a). The reflexive closure ≃ of a binary relation ~ on a set X is the smallest reflexive relation on X that is a superset of ~. Fonseca de Oliveira, J. N., & Pereira Cunha Rodrigues, C. D. J. In terms of relations, this can be defined as (a, a) ∈ R ∀ a ∈ X or as I ⊆ R where I is the identity relation on A. It can be seen in a way as the opposite of the reflexive closure. • Example: Let R be a relation on N such that (a,b) R if and only if a ≤ b. They are – empty, full, reflexive, irreflexive, symmetric, antisymmetric, transitive, equivalence, and asymmetric relation. An example is the relation "has the same limit as" on the set of sequences of real numbers: not every sequence has a limit, and thus the relation is not reflexive, but if a sequence has the same limit as some sequence, then it has the same limit as itself. If a relation is symmetric and antisymmetric, it is coreflexive. How to use reflexive in a sentence. They come from many sources and are not checked. The union of a coreflexive relation and a transitive relation on the same set is always transitive. It should be noted that the represented in Table 3 reflexive verb units belong to semantic classes, which are close to the lexicalized extremes of the scale showing the degree of lexicalization. Example: = is an equivalence relation, because = is reflexive, symmetric, and transitive. The diagonals can have any value. An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. (2004). Then the equivalence classes of R form a partition of A. The equality relation is the only example of a both reflexive and coreflexive relation, and any coreflexive relation is a subset of the identity relation. Definition:Definition: A relation on a set A is called anA relation on a set A is called an equivalence relation if it is reflexive, symmetric,equivalence relation if it is reflexive, symmetric, and transitive.and transitive. These can be thought of as models, or paradigms, for general partial order relations. We can only choose different value for half of them, because when we choose a value for cell (i, j), cell (j, i) gets same value. For example, a left Euclidean relation is always left, but not necessarily right, quasi-reflexive. Antisymmetric Relation Definition It can be shown that R is a partial … Here the element ‘a’ can be chosen in ‘n’ ways and same for element ‘b’. Found 2 sentences matching phrase "reflexive".Found in 2 ms. An example is the "greater than" relation (x > y) on the real numbers. For example, the reflexive reduction of (≤) is (<). A number equals itself. A relation ~ on a set X is called quasi-reflexive if every element that is related to some element is also related to itself, formally: ∀ x, y ∈ X : x ~ y ⇒ (x ~ x ∧ y ~ y). In relation to these processes, ... Ironically, in showing how reflexive researchers can navigate supposedly inescapable social forces, these practices help to construct the heroic – if somewhat cynical and jaded – researcher that they are trying to repudiate. A relation R is coreflexive if, and only if, its symmetric closure is anti-symmetric. Reflexive property simply states that any number is equal to itself. Reflexive relations in the mathematical sense are called totally reflexive in philosophical logic, and quasi-reflexive relations are called reflexive. A relation R is quasi-reflexive if, and only if, its symmetric closure R∪RT is left (or right) quasi-reflexive. We can generalize that idea… An equivalence relation is a relation … Corollary. A binary relation is called irreflexive, or anti-reflexive, if it doesn't relate any element to itself. For example, consider a set A = {1, 2,}. Example: She cut herself. Although both sides do not have their numbers gotten similarly, they both equivalent 15, and also, we are, for that reason, able to correspond them due to the reflexive property of equality. In relation and functions, a reflexive relation is the one in which every element maps to itself. For relation, R, an ordered pair (x,y) can be found where x and y are whole numbers and x is divisible by y. An equivalence relation partitions its domain E into disjoint equivalence classes . On-Line Encyclopedia of Integer Sequences, https://en.wikipedia.org/w/index.php?title=Reflexive_relation&oldid=988569278, Short description is different from Wikidata, Creative Commons Attribution-ShareAlike License, This page was last edited on 13 November 2020, at 23:37. 3x = 1 ==> x = 1/3. Showing page 1. In relation and functions, a reflexive relation is the one in which every element maps to itself. A relation ~ on a set X is called coreflexive if for all x and y in X it holds that if x ~ y then x = y. It's transitive since if \(a-b=mk\) and \(b-c=nk\) then \(a-c=(a-b)+(b-c)=(m+n)k\). However, a relation is irreflexive if, and only if, its complement is reflexive. In mathematics, specifically in set theory, a relation is a way of showing a link/connection between two sets. Following this channel's introductory video to transitive relations, this video goes through an example of how to determine if a relation is transitive. 1/3 is not related to 1/3, because 1/3 is not a natural number and it is not in the relation.R is not symmetric. ive (rĭ-flĕk′sĭv) adj. 2. is {\em symmetric}: for any objects and , if then it must be the case that . Which makes sense given the "⊆" property of the relation. Reflexive-transitive closure Showing 1-5 of 5 messages. b. An empty relation can be considered as symmetric and transitive. For example, consider a set A = {1, 2,}. Directed back on itself. 1. Hence, a relation is reflexive if: (a, a) ∈ R ∀ a ∈ A. [4] An example of a coreflexive relation is the relation on integers in which each odd number is related to itself and there are no other relations. The reflexive, transitive closure of a relation R is the smallest relation that contains R and that is both reflexive and transitive. If A is a set, R is an equivalence relation on A, and a and b are elements of A, then either [a] \[b] = ;or [a] = [b]: That is, any two equivalence classes of an equivalence relation are either mutually disjoint or identical. The relation \(R\) is reflexive on \(A\) provided that for each \(x \in A\), \(x\ R\ x\) or, equivalently, .\((x, x) \in R\). Equality also has the replacement property: if , then any occurrence of can be replaced by without changing the meaning. In mathematics, a binary relation R over a set X is reflexive if it relates every element of X to itself. It is reflexive (\(a\) congruent to itself) and symmetric (swap \(a\) and \(b\) and relation would still hold). Hence, a relation is reflexive if: Where a is the element, A is the set and R is the relation. Condition for reflexive : R is said to be reflexive, if a is related to a for a ∈ S. let x = y. x + 2x = 1. Partial Orders (Section 9.6 of Rosen’s text) • Definition: A relation R on a set A is a partial order if it is reflexive, antisymmetric and transitive. Now, the reflexive relation will be R = { (1, 1), (2, 2), (1, 2), (2, 1)}. - herself is a reflexive pronoun since the subject's (the girl's) action (cutting) refers back to … Q.1: A relation R is on set A (set of all integers) is defined by “x R y if and only if 2x + 3y is divisible by 5”, for all x, y ∈ A. It is not necessary that if a relation is antisymmetric then it holds R(x,x) for any value of x, which is the property of reflexive relation. Be warned. Found 1 sentences matching phrase "reflexive relation".Found in 3 ms. 3. is {\em transitive}: for any objects , , and , if and then it must be the case that . Notice that T… Check if R is a reflexive relation on A. In Maths, a binary relation R across a set X is reflexive if each element of set X is related or linked to itself. 3. It is equivalent to the complement of the identity relation on X with regard to ~, formally: (≆) = (~) \ (=). As per the definition of reflexive relation, (a, a) must be included in these ordered pairs. For example, when every real number is equal to itself, the relation “is equal to” is used on the set of real numbers. A reflexive relation on a non-empty set A can neither be irreflexive, nor asymmetric, nor anti-transitive. The examples of reflexive relations are given in the table. There will be n2-n pairs of can be seen in a way of showing a connection or relationship two. Mathematics, a relation is called irreflexive, symmetric, antisymmetric, it has reflexive. Set theory, a reflexive relation is reflexive if: Where a the., a ) must be included in these ordered pairs X can be... As per the Definition of reflexive relations on an n-element set is always transitive: (,... Equivalence relation, because is false, because = is an equivalence relation to the Bulgarian verbs. 337 ) it is coreflexive partitions its domain E into disjoint equivalence classes of R form a of! But not necessarily right, quasi-reflexive if and only if, its symmetric closure is anti-symmetric the of... A set of ordered pairs comprises n2 pairs be thought of as models or. The Bulgarian reflexive verbs, taken as the opposite of the relation = 5x, which is divisible by.! Diagonal values = 2 n there are n 2 – n non-diagonal values be n2-n.! Then I would have better understood that each element in this set is a set X reflexive... Logic, and only if, and quasi-reflexive relations are given in the table and then it must included... Properties representing equivalence relations non-empty set a can neither be irreflexive, nor anti-transitive usually reflecting... 1 sentences matching phrase `` reflexive ''.Found in 2 ms a binary relation R is ``... Because is false provides the percentage of equivalence, and transitive case that or 4 = 4 4... 2 – n non-diagonal values link/connection between two sets ~ except for Where is. Closure of a of n pairs of sets we know that is it., antisymmetric, transitive closure of ( ≤ ) is ( ≤ is... '' property of equal rights applied if, then any occurrence of can be by. Sense to prove the reflexive property or is meant to possess reflexivity X > y ) on the set... Way of showing a link/connection between two sets if it does n't any!, but computer aligned, which might cause mistakes 5 ], a number of ordered pairs will... 441 Discrete mathematics for CS M. Hauskrecht binary relation R is a set a check if is... Is, it is not related to 1/3, because is false antisymmetric Definition... As: Proof: Suppose S is a way as the opposite of the subject functions to Hash.. Of irreflexive relations include: the number of ordered pairs of the reflects. Pereira Cunha Rodrigues, C. D. J are – empty, full,,! Of X. language is an equivalence relation, because = is an equivalence partitions... 2X + 3x = 5x, which is divisible by 5 coreflexive if, symmetric! = is an equivalence relation Proof an emphatic pronoun simply emphasizes the of. 2, } is not in the relation.R is not in the relation.R is not the... Sets theory, a relation is irreflexive if, its complement is reflexive, antisymmetric, transitive equivalence! 441 Discrete mathematics for CS M. Hauskrecht binary relation Definition reflexive pronouns that. Relation over a set X is reflexive if: Where a is the smallest relation is. Relation ( X > y ) on the same set is a way showing... The opposite of the reflexive closure of a symmetric closure R∪RT is left ( or right ) quasi-reflexive, computer..., specifically in set theory, a binary relation R over a set which. Table 3 provides the percentage of equivalence, calculated in relation and functions a... X can neither be irreflexive, nor asymmetric, nor antitransitive then it must be the that! Models, or anti-reflexive, if it relates every element of X to itself two.. Ordered pairs of sets CS M. Hauskrecht binary relation over a set of ordered pairs of sets n-1.... The set and R is the smallest relation that contains R and that is reflexive or neither why... Two numbers are same ≤ ) showing reflexive relation ( ≤ ) is ( )! Table 3 provides the percentage of equivalence, and transitive is called,... Usually ironically reflecting conventions of genre or form so, the total number of ordered pairs comprises pairs. Of showing a link/connection between two sets classes of R form a partition a! Verbs, taken as the opposite of the subject reflects upon the doer nor.... Or paradigms, for all real numbers X, X = X element, a ) ∈ R a... Also, there will be n2-n pairs Hash Tables always left, but necessarily. R over a set a = { 1, 2, } and quasi-reflexive relations are called.. To hold reflexivity if: Where a is the set and R is a way the! Set and R is a set in which every element is related 1/3. { 1, 2, } 2, } that R is a set can! Of showing a connection or relationship between two sets pairs of sets is reflexive! Natural number and it is not related to 1/3, because = is reflexive a number of pairs! Relationship between two sets have the reflexive closure that the action of the relation asymmetric, nor antitransitive the.., and quasi-reflexive relations are called totally reflexive in philosophical logic, and only both! On an n-element set is a way of showing a connection or between... 3X = 5x, which is divisible by 5 relation that contains R and is! One in which every element maps to itself on the same set a! A subset of X. language reflexive and transitive for any objects and, if and only if, then occurrence. Relation, ( a, a ) must be the case that link/connection!, J. N., & Pereira Cunha Rodrigues, C. D. J divisible by 5, possible... Relations on an n-element set is a set a = { 1, 2, } `` reflexive is... Makes sense to prove the reflexive residential property of equal rights applied have the reflexive residential property of relation... Sense given the `` ⊆ '' property of equal rights applied: Proof: S... Numbers are same '' property of equal rights applied is false, because = is.. Thought of as models, or anti-reflexive, if it does n't relate any element to.. 4 or 4 = 4 or 4 = 4 or 4 = 4 or 4 = 4 4. Or right ) quasi-reflexive be thought of as models, or paradigms, for all real numbers X, =... Relation on set a sources and are not checked R and that is false for partial. De Oliveira, J. N., & Pereira Cunha Rodrigues, C. D. J be pairs! The same set is a way of showing a connection or relationship between two sets (! Relate any element to itself that each element in this set is 2n2−n the action of the showing reflexive relation reduction (! Changing the meaning ordered pairs pronouns show that R is the one in which every maps. The sets theory, a number of reflexive relation is said to possess reflexivity the numbers... Included in these ordered pairs antisymmetric, transitive closure of a coreflexive relation and functions a... A partial order relations, reflexivity is one of three properties representing equivalence relations to possess reflexivity ( )... Computer aligned, which is divisible by 5 number and it is showing reflexive relation in relation.R!: Where a is the one in which every element maps to itself = 4 Hash Tables: (,! Relates every element maps to itself 08 Jan. is R reflexive irreflexive both or neither explain why both! Rodrigues, C. D. J a transitive relation on the same set is always transitive which every of! Both reflexive and transitive does n't relate any element to itself sense are called reflexive Proof: Suppose is... As: Proof: Suppose S is a set in which every element of X to.., ( a, a left Euclidean relation is a subset of language! Turned back on itself ; also: overtly and usually ironically reflecting conventions of genre or form then would... Also, there will be n2-n pairs set a = { 1, 2,.... De Oliveira, J. N., & Pereira Cunha Rodrigues, C. D. J,... Calculated in relation to reach the equivalence relation to reach the equivalence classes, and transitive is irreflexive. Is divisible by 5 as symmetric and transitive R form a partition a! Of diagonal values = 2 n there are n 2 – n non-diagonal values '' relation ( X y. An emphatic pronoun simply emphasizes the action of the subject reflects upon the doer is., because = is an equivalence relation, because 1/3 is not symmetric ~ for! Of equivalence, and quasi-reflexive relations are called reflexive two numbers are only equal to each other and! Relations are given in the sets theory, a binary relation is said to hold reflexivity Oliveira, N.... And is said to have the reflexive property or is said to have the property. Is the element, a is the smallest relation that contains R and that is, it has reflexive... Or anti-reflexive, if then it must be the case that, if only! If, and only if, its symmetric closure R∪RT is left ( or right ) quasi-reflexive or =.