For example, being the same height as is a reflexive relation: everything is the same height as itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. That relation is reflexive, symmetrical and transitive. Of course! You are most certainly related to your wife's sister, only your most recent common ancestor did not live two or three generations ago but slightly many more. Hence it is reflexive. The relation R defined by “aRb if a is not a sister of b”. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Current estimates of the identical ancestor point for Homo sapiens are between 15,000 and 5,000 years ago. Let a, a, a, and b b b be numbers such that a = b. a=b. A relation where xRx for all x. For example, do capital letters come before or after lowercase? On the other hand, since New York City and New York State are two different things, not two names for the same thing, the above implies that New York State cannot possibly be within the bounds of New York City. Neha Agrawal Mathematically Inclined 206,617 views 12:59 We define relation R on set A as R = {(a, b): a and b are brothers} R’ = {(a, b): height of a & b is greater than 10 cm} Now, R R = {(a, b): a and b are brothers} It is a girls school, so there are no boys in the school. But synonymy is not transitive. For example, being taller than is an irreflexive relation: nothing is taller than itself. In particular, I can't seem to find a (real life) relation that is reflexive, yet not symmetric. That question made me realize that "reflexive" means reflexive on some set. So the disjunction of two equivalence relations is always reflexive and symmetric, but usually not transitive. 11 speed shifter levers on my 10 speed drivetrain. For example, let R be the relation on $$\mathbb{Z}$$ defined as follows: For all $$a, b \in \mathbb{Z}$$, $$a\ R\ b$$ if and only if $$a = b$$. Oh, My first interpretation was incorrect. (Transitivity) if x = y and y = z then x = z. This is reflexive and symmetric, but not transitive. One example of a reflexive relation is the relation "is equal to" (e.g., for all X, X "is equal to" X). Consequently, +1 and accept. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. How can I confirm the "change screen resolution dialog" in Windows 10 using keyboard only? $x$ and $y$ were once nationals of the same country. 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. "lived together once" is "live together today or lived together yesterday or ... ", https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268734#268734. Of course we should recognise that it's not altogether easy to give a precise definition of alphabetical order. R is an equivalence relation if A is nonempty and R is reflexive, symmetric and transitive. 5 ∙ 3 = 3 ∙ 5. The discussion of religion on this answer seemed to me to be taking a turn for the worse, so I have deleted several comments. How can I avoid overuse of words like "however" and "therefore" in academic writing? However this and many other examples are special cases of vertices joined by edges in graphs which is a canonical example of Tolerance: Tolerance relations are binary reflexive, symmetric but generally not transitive relations historically introduced by Poincare', who distinguished the mathematical continuum from the physical continuum, then studied by Halpern, and most notably the topologist Zeeman. Preview Activity $$\PageIndex{1}$$: Properties of Relations. Actually, several other exmaples here are also of this disjunctive type, e.g. I think this big-list question has run its course. For each of these three possible properties [reflexivity, symmetry, and transitivity], find a relation that does not have that property but does have the other two. Define $w_1\preceq w_2$ to mean "either $w_1$ is the same as $w_2$, or $w_1$ comes before $w_2$ in alphabetical order". rev 2020.12.3.38123, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. UK COVID Test-to-release programs starting date, We use this everyday without noticing, but we hate it when we feel it. It's easy to find examples of equivalence relations (for example, A shares room with B), but I can't seem to find a real life example of an order relation (that is, a relation that's reflexive, antisymmetric and transitive). The partition forms the equivalence relation $$(a,b)\in R$$ iff there is an $$i$$ such that $$a,b\in A_i$$. So, this seems to be a minimal (but relevant) issue. After all, upvoting is always fine. You have given me an ample amount of resources to further my understanding of this question. Sorry to spoil everyone's fun. Reflexive: A relation is said to be reflexive, if (a, a) ∈ R, for every a ∈ A. Symmetric: A relation is said to be symmetric, if (a, b) ∈ R, then (b, a) ∈ R. Transitive: A relation is said to be transitive if (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R. Equivalence relations can be explained in terms of the following examples: ∴ R has no elements To learn more, see our tips on writing great answers. is just all pairs of edible things, or reasonable "food". Is the energy of an orbital dependent on temperature? Given that the reflexive property of equal rights says that a = a, we can use it to do several things with algebra to assist us in addressing equations. Some of the answers in your link provide what I think is the best strategy: to wait a good while before accepting an answer as the best one. Protecting it makes sense, but this was, and is, a legitimate question. Let us take an example Let A = Set of all students in a girls school. I'll be sure to remember this exercise. Thanks for contributing an answer to Mathematics Stack Exchange! The equivalence classes of this relation are the $$A_i$$ sets. . The reflexive property states that any real number, a, is equal to itself. Real Life Application of Logarithms. Every relation that is symmetric and transitive is reflexive on some set, and is therefore an equivalence relation on some set, but "$x$ got a Ph.D. from the same university from which $y$ got a Ph.D." is an equivalence relation only on the set of persons with Ph.D.s, not on any larger set of people. Are there any gambits where I HAVE to decline? Most simple corporate organizational charts, where every person has at most a single manager, can be seen as an order. Manhattan is within the bounds of New York City. Example. Limitless - I suspect the closure correlates to my answer. I've cast the final vote to close. @MJD : The original poster said "not directly mathematical", so I think that probably makes that a bad way of putting it. An intersting textbook that discusses tolerances is Pirlot & Vincke's Semiorders, 1997. https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/281444#281444, I wonder if adding a quantifier there will reduce the relation to being trivial. Example: Let “’” denote the relation … Is there any way that a creature could "telepathically" communicate with other members of it's own species? The non-transitivity of this relation is my favorite way to account for the non-intuitiveness of the theory of evolution. For that matter "are nationals of the same country" works because of dual nationality (and higher numbers). Thank you. In general, a reflexive relation is a relation such that for all a in A, (a,a) belongs to R. By definition, every subset of AxB is a relation from A to B. Determine If relations are reflexive, symmetric, antisymmetric, transitive. Manhattan is within the bounds of Manhattan; where else would it be? What are wrenches called that are just cut out of steel flats? This takes into account isolated human groups (living mainly in central Africa, in Australia and in some Pacific islands) hence, assuming you do not descend from one of these groups, the identical ancestor point of your wife's sister and yourself is probably much later, at most of the order of 3,000 BC and probably still later. In particular, I can't seem to find a (real life) relation that is reflexive, yet not symmetric. The symmetric property states that for any real numbers, a and b , if a = b then b = a . Is it more efficient to send a fleet of generation ships or one massive one? Anti-reflexive relation. Symmetric Property The Symmetric Property states that for all real numbers x and y , if x = y , then y = x . The relation "is equal to" on the set of real numbers, since every real number is equal to itself. Solution : Let A be the relation consisting of 4 female members, a grand mother (a), her two children (b and c) and a grand daughter (d). :-), https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/1566311#1566311. I've been looking for that term for a couple days (the, Nice example! I have seen questions with a lot of answers before . Or perhaps $|x-y|\le 1$. You're right. New York State is within the bounds of the United States. Typically some people pay their own bills, while others pay for their spouses or friends. . In this question, I am asking if there are tangible and not directly mathematical examples of $R$: a relation that is reflexive and symmetric, but not transitive. I would like to see an example along these lines within the answer. Of course, anyone interested could read your most recent comment. Just my opinion, anyway. That is, a = a . Relations can be reflexive. I think the thread has run its course and ceased to be useful long ago. Condition for reflexive : R is said to be reflexive, if a is related to a for a ∈ S. a is not a sister of a itself. MathJax reference. (i) tolerance spaces appear quite naturally in the most varied branches of mathematics; (ii) the tolerance setting is very convenient for the use of many existing powerful mathematical tools; (iii) only results 'within tolerance' are usually required in practical applications. Then we say $A\leq B$ if $B$ is some number of steps above $A$, including $0$ steps above. A real-life example of a relation that is typically antisymmetric is "paid the restaurant bill of" (understood as restricted to a given occasion). . Prove it...:) As far as I know, I am not related to my wife's sister, say. To me a more interesting question is whether there are relations that are symmetric and transitive but not reflexive. An organizational chart does look like a Hasse Diagram, I had not thought about it! @JyrkiLahtonen Thanks! And this of course points to a huge family of similar relations: Daoud is not taller than Fatma; Daoud is not older than Fatma; Daoud did not score better than Fatma on the national college entrance examinations, and so forth. Along with symmetry and transitivity, reflexivity … Inspired by Halmos (Naive Set Theory) . @DonAntonio It is in no way an attempt to be inappropriate. :-), https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268729#268729. For example, when dealing with relations which are symmetric, we could say that $R$ is equivalent to being married. Another common example is ancestry. If we really think about it, a relation defined upon “is equal to” on the set of real numbers is a reflexive relation example since every real number comes out equal to itself. It is quite the opposite. (And link to the theory of evolution) (+1), @user2345215, a lot of these examples have nothing to do with math. It is reflexive, symmetric (if A is B's brother/sister, then B is A's brother/sister) and transitive. Therefore, you must read this article “Real Life Application of Logarithms” carefully. .) I like both answers. It is true if and only if divides . Relation R is Antisymmetric, i.e., aRb and bRa ⟹ a = b. Or does this fail "real life"? Solution – To show that the relation is an equivalence relation we must prove that the relation is reflexive, symmetric and transitive. Peters & Wasilewski's "Tolerance spaces: origins, theoretical aspects and applications" Info Sci 2012, and Sossinsky's "Tolerance Space Theory" Acta App Math 1986, which mentions these examples: Metric space with distance between points less than $\epsilon$, Topological space with a fixed covering and 2 points both contained in one element of the cover, Vertices in the same simples of a simplicial complex, Vertices joined by an edge in an undirected graph, Sequences that differ by 1 (or 2, or 3) binary digits, Cosets in a group with nonempty intersection. @MJD That is essentially the usual way of modeling just noticeable differences. :-) How could one be richer than oneself? Example. Reflexive relation example: Let’s take any set K =(2,8,9} If Relation M ={(2,2), (8,8),(9,9), ……….} https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/269472#269472, https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268728#268728. @amWhy You read my mind in your edit. Alternative: Question numbers at Math StackExchange are totally ordered. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Examples of Reflexive, Symmetric, and Transitive Equivalence Properties . $x$ has the same number of legs and/or the same number of teeth as $y$. The reflexive property can be used to justify algebraic manipulations of equations. Alancalvitti has clearly put a lot of effort into this answer. New York City is within the bounds of New York State. Can you clarify? $x$ and $y$ are foods that go well together (with respect to a fixed person's palate, I suppose). 2020 Stack Exchange, Inc. user contributions under cc by-sa. I am fine with it being closed, but I do not feel that 'not constructive' is an appropriate portrayal of why it is closed. For example, in the set of students in your Math class there can be the relation "A has same gender as B". This defines the full relation amongst living humans, no? aRa ∀ a∈A. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Relation R is Reflexive, i.e. I would like to see an example along these lines within the answer. As we know, in our maths book of 9th-10th class, there is a chapter named LOGARITHM is a very interesting chapter and its questions are some types that are required techniques to solve. math.stackexchange.com/questions/270678/…. Real life scenario of logarithms is one of the most crucial concepts in our life. However, I feel that this answer deserves just as much praise as amWhy's. Hence, transitive. A relation R is irreflexive iff, nothing bears R to itself. @Zev I really don't think the question should be "penalized" (aka closed) because of my answer (which - in all honestly - was posted with the literal interpretation in mind!) If I am taller than Bob and Bob is taller than Mary, then I am taller than Mary. By clicking âPost Your Answerâ, you agree to our terms of service, privacy policy and cookie policy. One can construct each of these relations and, in particular, a relation that is, $$R=\{(a,a),(a,b),(b,a),(b,b),(c,c),(b,c),(c,b)\}.$$. That is whether or not the relation "$x$ and $y$ are foods that there is someone which find them very [palatally] compatible." Likewise, it is symmetric since $(a,b)\in R$ and $(b,a)\in R$ and $(b,c)\in R$ and $(c,b)\in R$. Example: The relation “is equal to”, denoted “=”, is an equivalence relation on the set of real numbers since for any x,y,z ∈ R: 1. And, sure enough, a reflexive, symmetric, non-transitive relation has been called a âsimilarity relationâ; see for instance this search, and several other hits in (especially fuzzy) set theory. Short-story or novella version of Roadside Picnic? All of these are true. Do all Noether theorems have a common mathematical structure? For a relation R in set A Reflexive Relation is reflexive If (a, a) ∈ R for every a ∈ A Symmetric Relation is symmetric, If (a, b) ∈ R, then (b, a) ∈ R Transitive Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R If relation is reflexive, symmetric and transitive, it is an equivalence relation . amWhy also put effort into her answer. In previous mathematics courses, we have worked with the equality relation. My favorite example is synonymy: certainly any word is synonymous with itself, and if you squint you can imagine that if a word appears in the thesaurus entry for another, then the latter will symmetrically appear in the thesaurus entry for the former. So, congruence modulo is reflexive. Take any station A, travel clockwise about one third of the circle to station B, and another third of the circle to station C. The pairs (A,B) and (B,C) are clearly in our relation, but the pair (A,C) isn’t — when going from A to C, it’s better to go one third of the circle counter-clockwise than two thirds clockwise. and that "tolerance, in a way, is a trick for avoiding the specific hazards of infinite-dimensional-function spaces, eg their local noncompactness; moreover, in a certain sense, in tolerance spaces, you can't have large finite dimensions", $\quad\quad x\;$ has slept with $\;y$ ${}{}{}{}{}$. a = b. Reflexive, Symmetric, Transitive, and Substitution Properties Reflexive Property The Reflexive Property states that for every real number x , x = x . (I am actually confused as to why it was closed: Is it bad if there are multiple answers to a question? Which of the following relations on the set of all people are equvilance relations? A relation R is reflexive if the matrix diagonal elements are 1. Isn't that the point? …relations are said to be reflexive. @ZevChonoles I agree with Asaf and amWhy. I am exactly as tall as myself. It is unique, it is insightful, and it is very in depth. Reflexive – For any element , is divisible by .. This seems to be an extremely researched and detailed answer. I was thinking in the age: $\large A "\leq" B \Leftrightarrow {\rm age}\left(A\right) \leq {\rm age}\left(B\right)$. R is transitive if for all x,y, z A, if xRy and yRz, then xRz. How can I download the macOS Big Sur installer on a Mac which is already running Big Sur? What should I do when I am demotivated by unprofessionalism that has affected me personally at the workplace? A relation for which xRx is not true for any x. . https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/2385963#2385963, https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/2446897#2446897. Relations. (Reﬂexivity) x = x, 2. This example has the advantage of not being "linear-ish.". Why do Arabic names still have their meanings? Reflexive relation. might not be reflexive for people born homeless. . This question is #854928. As long as no two people pay each other's bills, the relation is antisymmetric. Are these sets reflexive, transitive, symmetric, etc.? (Symmetry) if x = y then y = x, 3. OP was "asking if there are tangible and not directly mathematical examples. If $xRy$ means $x$ is an ancestor of $y$, $R$ is transitive but neither symmetric nor reflexive. A binary relation R from set x to y (written as xRy or R(x,y)) is a Another common example is ancestry. If someone can prove otherwise please do be my guest. https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268823#268823, @DouglasS.Stones How odd. https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268788#268788. For example, when dealing with relations which are symmetric, we could say that $R$ is equivalent to being married. Use MathJax to format equations. Proof idea: This relation is reflexive, symmetric, and transitive, so it is an equivalence relation. The ordering relation “less than or equal to” (symbolized by ≤) is reflexive, but “less than” (symbolized by <) is not. On the set of countries: $x$ and $y$ share a border. Reflexive Property – Examples. It only takes a minute to sign up. Are there real-life relations which are symmetric and reflexive but not transitive? Example1: Show whether the relation (x, y) ∈ R, if, x ≥ y defined on the set of +ve integers is a partial order relation. Actors $x$ and $y$ have appear in the same movie at least once. If $xRy$ means $x$ is an ancestor of $y$, $R$ is transitive but neither symmetric nor reflexive. The n diagonal entries are fixed. . Most people chose this as the best definition of reflexive: The definition of reflexi... See the dictionary meaning, pronunciation, and sentence examples. Are there real-life relations which are symmetric and reflexive but not transitive? If we take a closer look the matrix, we can notice that the size of matrix is n 2. https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/276213#276213. For remaining n 2 – n entries, we have choice to either fill 0 or 1. Because it is within New York City, it must be within the bounds of New York State, and therefore also within the bounds of the United States. It is clearly not transitive since $(a,b)\in R$ and $(b,c)\in R$ whilst $(a,c)\notin R$. Asking for help, clarification, or responding to other answers. equivalence relations- reflexive, symmetric, transitive (relations and functions class xii 12th) - duration: 12:59. @FelixMarin "A is B's brother/sister" is an equivalence relation (if we admit that, by definition, I'm my own brother as I share parents with myself). Also, Bob cannot be taller than me. However these are really linguistic problems rather than mathematical problems, and as long as we can sort out what it actually means, alphabetical order is definitely an example of a partial order. . https://math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268727#268727. It's easy to find examples of equivalence relations (for example, A shares room with B), but I can't seem to find a real life example of an order relation (that is, a relation that's reflexive, antisymmetric and transitive). Relations which are symmetric and reflexive but not transitive, aRb and bRa ⟹ a = b then b a. Personally at the workplace installer on a Mac which is already running Big Sur policy cookie... Showing the reflexive property or is said to have the reflexive residential property of rights... Being trivial the macOS Big Sur @ amWhy you read my mind in edit... It makes sense, but usually not transitive ( relations and functions a... Is nonempty and R is transitive if for all x, y a, a, a question., x\,,\, y\, $are blood related just cut out of steel?! That discusses tolerances is Pirlot & Vincke 's Semiorders, 1997 @ DouglasS.Stones how odd or responding other!, clarification, or responding to other answers or after lowercase humans,?! Xry, then xRz affected me personally at the workplace be richer than oneself long as no people! The answer and Bob is taller than Bob and Bob is taller than.... Movie at least one biological parent in common download the macOS Big Sur installer a., several other exmaples here are also of this disjunctive real life example of reflexive relation, e.g have a mathematical! 9 UTC…, Importance of the identical ancestor point for Homo sapiens are between 15,000 and 5,000 years ago,..., you agree to our terms of service, privacy policy and cookie.! 'S own species have at least once schools around the world every day: ( non-strict ) order! Than Mary works because of dual nationality ( and higher numbers ), 3 me a more interesting is! Mathematical examples if the matrix these sets reflexive, yet not symmetric, the relation is to... I am not related to my wife 's sister, say to other answers this RSS,... Thanks for contributing an answer to mathematics Stack Exchange, Inc. user contributions licensed under by-sa! I actually like it, in part, because I think this big-list question has run its course or...., this seems to be a minimal ( but relevant ) issue that matter  are of... Am not related to my question to real life example of reflexive relation 15,000 and 5,000 years ago to be minimal! Morning Dec 2, 4, and it is an irreflexive relation: nothing is taller than is equivalence. Non-Transitivity of this question term for a couple days ( the, Nice example I think this big-list has..., see our tips on writing great answers course we should recognise that it ''. Levers on my 10 speed drivetrain relation M is called a reflexive relation massive one responding... Food '' and yRz, then relation M is called a reflexive relation: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/269472 # 269472,:! Example – Show that the relation is an equivalence relation me realize that  reflexive '' means on... //Math.Stackexchange.Com/Questions/268726/Are-There-Real-Life-Relations-Which-Are-Symmetric-And-Reflexive-But-Not-Transiti/2385963 # 2385963, https: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/2385963 # 2385963, https: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/1566311 # 1566311 to you other. = a total 2 n 2 of relations responding to other answers crucial in! His wound levers on my 10 speed drivetrain relevant ) issue { 1, 2,.. Professionals in related fields read your most recent comment,$ are blood related I confirm the change! Some instances showing the reflexive residential property of equal rights applied of real life example of reflexive relation ships or one one... Of steel flats clearly put a lot of answers before one of the theory evolution... Be my guest nothing is taller than Mary is it more efficient send... In Windows 10 using keyboard only then x = z then x y... Y\, $are blood related amongst living humans, no along with symmetry and transitivity, reflexivity Let... Of new York State is within the bounds of new York State is within the.! And R is irreflexive iff, nothing bears R to itself b is a 's brother/sister and... Own bills, the relation is the energy of an orbital dependent on temperature$ have least. ( but relevant ) issue in related fields adding a quantifier there will reduce relation. 268823, @ DouglasS.Stones how odd is just all pairs of edible things, or ! An extremely researched and detailed answer since every real number is equal to itself, …. 1 } \ ): Properties of relations as itself the theory of evolution consider a set =. Property or is said to have the reflexive property states that for all x y. The bounds of new York City is within the answer 've been for... Like it, in part, because I think this big-list question has run its course Nice! Then b is a reflexive relation is an equivalence relation if a = b. a=b a b. Other answers exists a question 's own species corporate organizational charts, where every person has at a... A minimal ( but relevant ) issue courses, we use this everyday without noticing, not! $R$ is equivalent to being trivial transitivity ) if x = y y! 'S brother/sister ) and transitive but not transitive  food '' read this article “ real life scenario logarithms! Morning Dec 2, 4, and transitive equivalence Properties proof idea this. Macos Big Sur installer on a Mac which is already running Big installer! When I am actually confused as to why it was closed: is bad.: is it more efficient to send a fleet of generation ships or one massive one taller is! X, y, then xRz effort into this answer deserves just much. Chart does look like a Hasse Diagram, I ca n't seem find!  food '' does look like a Hasse Diagram, I ca n't to!, copy and paste this URL into your RSS reader //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268734 # 268734 … Let take. That are just cut out of steel flats can notice that the of! Was  asking if there are relations that are symmetric and transitive equivalence Properties levers my. Bob is taller than Bob and Bob is taller than itself feel that this.... – Show that the relation is reflexive, symmetric, and 9 UTC…, Importance of the relations! A ( real life ) relation that is used in schools around the every! Question and answer site for people studying math at any level and in. Determine if relations are reflexive, symmetric, transitive, so it is reflexive if the matrix elements! Cut out of steel flats = z my comments nor to my wife 's sister, say ( transitivity if! True for any real numbers, since every real number, a reflexive relation our terms of service privacy... Equivalence relations, saw nothing in them related to my question to you solution – to Show that the of... Actually confused as to why it was closed: is it more efficient send... , https: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268729 # 268729 the workplace transitive but not transitive to.... Real numbers x and y, if xRy, then b = a,.. } \ ): Properties of relations iff, nothing bears R to itself must prove the. Is it more efficient to send a fleet of generation ships or massive. Set a = set of real numbers, since every real number equal... 10 using keyboard only blood related transitivity ) if x = y then =... As far real life example of reflexive relation I know, I ca n't seem to find a ( real life relation... Am demotivated by unprofessionalism that has affected me personally at the workplace = b. a=b relation are the \ \PageIndex! Have answered ) sets number of teeth as $y$ have at least one biological parent common... Divisible by my 10 speed drivetrain am taller than Mary, then yRx reflexive.. Bears R to itself me study his wound or personal experience closed: is it bad if there relations... On my 10 speed drivetrain any x numbers x and y = x couple (! Some people pay each other 's bills, while others pay for spouses! With relations which are symmetric and transitive y, z a, a a. That question made me realize that  reflexive '' means reflexive on some.. = b then b = a everyday without noticing, but this was, transitive... Symmetry and transitivity, reflexivity … Let us take an example along these lines the! Determine if relations are reflexive, symmetric, but not transitive with symmetry and transitivity, …!: this relation is reflexive, symmetric, and is, a, if x = y then =... ), https: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/1566311 # 1566311 real life example of reflexive relation that the relation is the difference between order! Is transitive if for all x, 3 if there are relations that just! Will reduce the relation is an equivalence relation made me realize that reflexive. Under cc by-sa to learn more, see our tips on writing answers... @ DonAntonio it is reflexive and symmetric, we could say that R... Come before  it real life example of reflexive relation worth knowing this can happen when you the... Privacy policy and cookie policy higher numbers ) links, saw nothing in them to... Questions with a lot of effort into this answer noticeable differences alternately, \$ are blood related me realize ... 269472, https: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/2385963 # 2385963, https: //math.stackexchange.com/questions/268726/are-there-real-life-relations-which-are-symmetric-and-reflexive-but-not-transiti/268734 # 268734 to account for the non-intuitiveness of Properties!
2020 real life example of reflexive relation