a For instance, answers to code-golf challenges should attempt to be as short as possible. and hence x Let us consider the set A as given below. @isaacg that's what I meant. Code Golf Stack Exchange is a question and answer site for programming puzzle enthusiasts and code golfers. You will be given a list of pairs of integers in any reasonable format. You could set up the relation as a table of ordered pairs. Does the input have to be a list-like format, or can it be an adjacency--matrix-like format? then there are no such elements X How to explain why I am applying to a different PhD program without sounding rude? For instance, while "equal to" is transitive, "not equal to" is only transitive on sets with at most one element. Challenges must have, Code Golf 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. (Transitive – put off) 10. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considered. How to determine if MacBook Pro has peaked? = So, if A=5 for instance, then B and C must both also be 5 by the transitive … b We had to put off our visit to France. Truthy is the input list, falsy is 0. def reflexive(R): """ Determine whether the binary relation R on a set A is reflexive, and if so, which elements of R are essential for it to be reflexive. However, please refrain from exploiting obvious loopholes. A relation is a transitive relation if, whenever it relates some A to some B, which B to some C, it also relates that A thereto C. Some authors call a relation intransitive if it's not transitive. A transitive verb is one that only makes sense if it exerts its action on an object. A verb can be described as transitive or intransitive based on whether it requires an object to express a complete thought or not. Output: a truthy value for a transitive relation, falsy otherwise. X It only takes a minute to sign up. Condition for transitive : R is said to be transitive if “a is related to b and b is related to c” implies that a is related to c. aRc that is, a is not a sister of c. cRb that is, c is not a sister of b. How can I prevent cheating in my collecting and trading game? You may assume that the input will consist of at least one pair, and that the pairs are unique. For instance, "was born before or has the same first name as" is not a transitive relation, since e.g. , while if the ordered pair is not of the form The transitive extension of R, denoted R1, is the smallest binary relation on X such that R1 contains R, and if (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R1. For example, if Amy is an ancestor of Becky, and Becky is an ancestor of Carrie, then Amy, too, is an ancestor of Carrie. x As unnamed lambda returning via reference parameter. This input has to be a set of two-element vectors: If input must be list-like then (%[a d]) has to be replaced by ((set %)[a d]) for extra 6 bytes. Podcast 301: What can you program in just one tweet? Combining Relation: Suppose R is a relation from set A to B and S is a relation from set B to C, the combination of both the relations is the relation which consists of ordered pairs (a,c) where a Є A and c Є C and there exist an element b Є B for which (a,b) Є R and (b,c) Є S. {\displaystyle aRb} , This paper studies the transitive incline matrices in detail. …Be sure to follow the challenge specification. To see that every a ∈ A belongs to at least one equivalence class, consider any a ∈ A and the equivalence class[a] R ={x What is more, it is antitransitive: Alice can never be the birth parent of Claire. a I think your confusion here stems from misinterpreting negative transitivity to mean "not transitive". Transitive definition is - characterized by having or containing a direct object. Modulo Challenge (Addition and Subtraction) Modular multiplication. (Beware: some authors do not use the term codomain(range), and use the term range inst… Full list of "special cases" during Bitcoin Script execution (p2sh, p2wsh, etc.)? R I'm pretty sure that a 1-0 matrix representing a matrix is transitive a_ij= 1 == a_ji=1 implies that a_ii == 1 for a matrix a(not sure though). Update: Instead of using :when I'll just check that for all pairs of [a b] [c d] either b != c or [a d] is found from the input set. How do you detect and defend against micro blackhole cannon? No general formula that counts the number of transitive relations on a finite set (sequence A006905 in the OEIS) is known. Practice: Modular addition. TRANSITIVE RELATION. {\displaystyle (x,x)} (Bought – transitive) 7. This question hasn't been answered yet Ask an expert ∈ The intersection of two transitive relations is always 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. …Include a short header which indicates the language(s) of your code and its score, as defined by the challenge. [(7, 8), (9, 10), (15, -5)] is transitive, because there aren't any two pairs (Changed – transitive) 8. [18], Transitive extensions and transitive closure, Relation properties that require transitivity, harvnb error: no target: CITEREFSmithEggenSt._Andre2006 (, Learn how and when to remove this template message, https://courses.engr.illinois.edu/cs173/sp2011/Lectures/relations.pdf, "Transitive relations, topologies and partial orders", Counting unlabelled topologies and transitive relations, https://en.wikipedia.org/w/index.php?title=Transitive_relation&oldid=995080983, Articles needing additional references from October 2013, All articles needing additional references, Creative Commons Attribution-ShareAlike License, "is a member of the set" (symbolized as "∈"). [16], Generalized to stochastic versions (stochastic transitivity), the study of transitivity finds applications of in decision theory, psychometrics and utility models. Is there any hope of getting my pictures back after an iPhone factory reset some day in the future? The relation is not transitive if we can find (A,B) and (B,C) such that (A,C) doesn't hold. How can I fill two or more adjacent spaces on a QO panel? The relation is transitive : … For instance, within the organic phenomenon, wolves prey on deer, and deer prey on grass, but wolves don't prey on the grass. , , R is an iterable of homogeneous pairs. As a native speaker, I would say "prove that big-O is transitive as a relation" if I wanted to tell somebody "prove that the relation $\{f,g\mid f=O(g)\}$ is transitive". [15] Unexpected examples of intransitivity arise in situations such as political questions or group preferences. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. x To find out whether a verb is transitive or intransitive, you should examine how it is connected with other words in the sentence, namely it is important to look for an object. x Theorem: Let R be an equivalence relation over a set A.Then every element of A belongs to exactly one equivalence class. {\displaystyle a,b,c\in X} From those values it generates the adjacency matrix; matrix-multiplies it by itself; and converts nonzero values in the result matrix to ones. Falsy is a matrix that contains at least one zero. Did the Germans ever use captured Allied aircraft against the Allies? Some people mistakenly refer to the range as the codomain(range), but as we will see, that really means the set of all possible outputs—even values that the relation does not actually use. Determining if a 1-0 matrix that represents a relation is transitive. Truthy output is a matrix formed by ones. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. -12 bytes thanks to Bubbler. a relation is called transitive if for any two pairs of elements (a, b) and (b, c) in this relation, a pair (a, c) is also present, [ (1, 2), (2, 4), (6, 5), (1, 4)] is transitive, because it contains (1, 2) and (2, 4), but (1, 4) as well, Proof: We will show that every a ∈ A belongs to at least one equivalence class and to at most one equivalence class. , Requires its input to be a container of pair. Some verbs may be used both ways. In other words, my test case is only truthy because the relation isn't implicitly symmetric. How to use transitive in a sentence. The complement of a transitive relation need not be transitive. A relation is in 3NF if at least one of the following condition holds in every non-trivial function dependency X –> Y: X is a super key. The transitive extension of this relation can be defined by (A, C) ∈ R1 if you can travel between towns A and C by using at most two roads. #~Permutations~{2}] creates the list of all ordered pairs of ordered pairs from the input, and Join@@@ converts those to ordered quadruples. {\displaystyle a,b,c\in X} Table[...,{i,#},{j,#}] creates a 2D array indexed by i and j, which are taken directly from the input (hence are both ordered pairs). x (Changed – intransitive) 9. In contrast, a relation R is called antitransitive if xRy and yRz always implies that xRz does not hold. Taking the boring O(n^3) approach. The intersection of two transitive relations is always transitive: knowing that "was born before" and "has the same first name as" are transitive, we can conclude that "was born before and also has the same first name as" is also transitive. c For example, on set X = {1,2,3}: Let R be a binary relation on set X. The quotient remainder theorem. Bob has changed a lot since he got married to Alice. Let R be the relation on towns where (A, B) ∈ R if there is a road directly linking town A and town B. (Has won – transitive) 6. Are there 300,000 items in the average American household, and 10,000 items in the average European household? Consider a relation. Both these solutions are unnamed functions taking a list of ordered pairs as input and returning True or False. X Online test suite. Finally, it checks that no entry in the latter matrix exceeds that in the adjacency matrix. for some Pfeiffer[9] has made some progress in this direction, expressing relations with combinations of these properties in terms of each other, but still calculating any one is difficult. ( Answers abusing any of the standard loopholes are considered invalid. The relation defined by xRy if x is the successor number of y is both intransitive[14] and antitransitive. [6] For example, suppose X is a set of towns, some of which are connected by roads. The function of those two indices is Last@i!=#&@@j||#~MemberQ~{#&@@i,Last@j}, which translates to "either the second element of i and the first element of j don't match, or else the input contains the ordered pair consisting of the first element of i and the last element of j". For instance, knowing that "was born before" and "has the same first name as" are transitive, one can conclude that "was born before and also has the same first name as" is also transitive. {\displaystyle x\in X} Improve running speed for DeleteDuplicates. The code first reduces the input integers to unique, 1-based integer values. ∈ If a relation is transitive then its transitive extension is itself, that is, if R is a transitive relation then R1 = R. The transitive extension of R1 would be denoted by R2, and continuing in this way, in general, the transitive extension of Ri would be Ri + 1. Can I repeatedly Awaken something in order to give it a variety of languages? This means than an agent makes the same choices whether she uses her preference relation, <, or her utility function u(x). b [10], A relation R is called intransitive if it is not transitive, that is, if xRy and yRz, but not xRz, for some x, y, z. If so, you have a function! But a is not a sister of b. $\endgroup$ – David Richerby Feb 13 '18 at 14:30 knowing that "is a subset of" is transitive and "is a supersetof" is its converse, we can conclude that the latter is transitive as well. Equivalence relations. Those are then operated upon by the function If[#2==#3,{#,#4},Nothing]&@@@, which has a cool property: if the middle two elements are equal, it returns the ordered pair consisting of the first and last numbers; otherwise it returns Nothing, a special Mathematica token that automatically disappears from lists. But, in any case, the question asks what "by relation" means and your answer doesn't say anything at all about that. Watch this tutorial to see how you can determine if a relation is a function. Ask Question Asked 6 years, 9 months ago. …Please make sure to answer the question and provide sufficient detail. . Given a list of pairs of integers, determine if a relation is transitive or not. This relation need not be transitive. {\displaystyle (x,x)} Language of the month for January 2021: Scala, Find maximal matching in divisibility relation, Equivalence classes on the Transitive Closure of a Reflexive Relation. c Explanations of your answer make it more interesting to read and are very much encouraged. A relation is said to be equivalence relation, if the relation is reflexive, symmetric and transitive. The problem is I am always returning true. Would Venusian Sunlight Be Too Much for Earth Plants? What is the difference between a transitive verb and an intransitive verb? An intransitive verb will make sense without one. Beethoven Piano Concerto No. a (Outer)loop over all pairs (a,b) and (inner)loop over the same pairs, now called (c,d) and every time when b==c check if (a,d)is also an existent pair. The transitive property comes from the transitive property of equality in mathematics. This is an anonymous block (function) which takes the elements as a two-level array, but the test suite does string manipulation to put the input into a suitable format first. @LeakyNun Oh whoops, that was supid stupid of me. For example relation IR on N such that " a R b " iff "a >=b^3" for all a,b € N I think it's antisymmetric but I don't know how to prove it The relation "is the birth parent of" on a set of people is not a transitive relation. Modular exponentiation. R A transitive relation need not be reflexive. Is it better for me to study chemistry or physics? This is the currently selected item. and It is perfectly possible for a binary relation to be both transitive and negatively transitive, as is the case here with the strict preference relation. R ∈ A homogeneous relation R on the set X is a transitive relation if,[1]. You never cease to amaze me. When it is, it is called a preorder. b How to detect real C64, TheC64, or VICE emulator in software? 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. R Transitive and intransitive verbs. A = {a, b, c} Let R be a transitive relation defined on the set A. If the input list contains {a,b} and {b,c} but not {a,c} for some a, b, c, replaces it with 0. Usage example: f [(1,2), (2,4), (6,5), (1,4)]-> True. a (b) A relation on $$A$$ that is transitive but not symmetric (c) A relation on $$A$$ that is symmetric and transitive but not reflexive on $$A$$ (d) A relation on $$A$$ that is not reflexive on $$A$$, is not symmetric, and is not transitive (e) A relation on $$A$$, other than the identity relation, that is an equivalence relation on $$A$$ ( On the other hand, "is the birth parent of" is not a transitive relation, because if Alice is the birth parent of Brenda, and Brenda is the birth parent of Claire, then Alice is not the birth parent of Claire. For example, likes is a non-transitive relation: if John likes Bill, and Bill likes Fred, there is no logical consequence concerning John liking Fred. x …Try to optimize your score. Then we return truthy from the inner predicate (falsey from the whole program) if [A:C] isn't there. {\displaystyle a,b,c\in X} b A relation is reflexive if and only if it contains (x,x) for all x in the base set. Active 6 years, 9 months ago. , b This page was last edited on 19 December 2020, at 03:08. @Lynn Check out the Prolog answer, then ;-), You might be able to shorten the second solution by making an abbreviation for, @Cyoce Indeed, you save 3 bytes each time by writing. Wow, Clojure for loops are cool :D This checks that the for loop does not generate a falsy value, which occurs if [a d] is not found from the input set. Question: How Can A Matrix Representation Of A Relation Be Used To Tell If The Relation Is: Reflexive, Irreflexive, Symmetric, Antisymmetric, Transitive? A transitive dependency exists when you have the following functional dependency pattern: A → B and B → C; therefore A → C This is precisely the case with the original items relation. Such relations are used in social choice theory or microeconomics. such that But that's not what it means. For instance, [(1, 2), (5, 1), (-9, 12), (0, 0), (3, 2)] is a relation. I don't think it means the pairs in an order - I think it means each pair has an order, first then second. Then there … rev 2021.1.5.38258, The best answers are voted up and rise to the top, Code Golf Stack Exchange is a site for recreational programming competitions, not general programming questions. Hence it is transitive. Definition 1. This article examines the concepts of a function and a relation. Then, test to see if each element in the domain is matched with exactly one element in the range. This creates a 2D array of booleans, which And@@And@@@ flattens into a single boolean. Combine the results with logical and. You should have a test case that is only transitive because the pairs are ordered. For the example of towns and roads above, (A, C) ∈ R* provided you can travel between towns A and C using any number of roads. a , A relation R is symmetric iff, if x is related by R to Theorem 1 (Utility Representation Theorem). a relation is called transitive if for any two pairs of elements (a, b) and (b, c) in this relation, a pair (a, c) is also present. c How to install deepin system monitor in Ubuntu. c Since only a, b, and c are in the base set, and the relation contains (a,a), (b,b), and (c,c), yes, it is reflexive. Symmetricity. In math, if A=B and B=C, then A=C. [7], The transitive closure of a relation is a transitive relation.[7]. 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. Symmetric, Transitive, and Reflexive Relations Date: 11/10/98 at 11:30:27 From: Mike Subject: Discrete math Suppose R is a symmetric and transitive relation on A. * 1NF means that all attribute values are atomic (data cannot be broken down further. where a R b is the infix notation for (a, b) ∈ R. As a nonmathematical example, the relation "is an ancestor of" is transitive. I don't know what you mean by "reflexive for a,a b,b and c,c. -24 bytes thanks to Leaky Nun 3: Last notes played by piano or not? A relation is any association or link between elements of one set, called the domain or (less formally) the set of inputs, and another set, called the range or set of outputs. , and indeed in this case How to tell if a relation is reflexive symmetric or transitive? Transitivity of generalized fuzzy matrices over a special type of semiring is considered. = [8] However, there is a formula for finding the number of relations that are simultaneously reflexive, symmetric, and transitive – in other words, equivalence relations – (sequence A000110 in the OEIS), those that are symmetric and transitive, those that are symmetric, transitive, and antisymmetric, and those that are total, transitive, and antisymmetric. If you think a specification is unclear or underspecified, comment on the question instead. Saved 2 bytes thanks to an idea by @Cyoce. Input format is a matrix (using ; as row separator) where each pair of the relation is a column. X Is 7/8 an example of measured rhythm or metrical rhythm? Previously, we have already discussed Relations and their basic types. b The union of two transitive relations is not always transitive. A relation R is non-transitive iff it is neither transitive nor intransitive. {\displaystyle R} , So the result is the set of ordered pairs that needs to be in the input for it to be transitive; SubsetQ[#,...] detects that property. Thanks! [(1, 2), (2, 4), (6, 5), (1, 4)] is transitive, because it contains (1, 2) and (2, 4), but (1, 4) as well. is vacuously transitive. I bought her some flowers. How do you figure out if a relation is a function? A relation R containing only one ordered pair is also transitive: if the ordered pair is of the form ∈ ) What Superman story was it where Lois Lane had to breathe liquids? Suppose the agent’s preferences, <, are com-plete and transitive, and that X is ﬂnite. Practice: Modular multiplication. [13] "Is greater than", "is at least as great as", and "is equal to" (equality) are transitive relations on various sets, for instance, the set of real numbers or the set of natural numbers: The empty relation on any set A relation is in third normal form, if there is no transitive dependency for non-prime attributes as well as it is in second normal form. X The union of two transitive relations need not be transitive. E.g. Viewed 764 times 0. However, in biology the need often arises to consider birth parenthood over an arbitrary number of generations: the relation "is a birth ancestor of" is a transitive relation and it is the transitive closure of the relation "is the birth parent of". = In mathematics, a homogeneous relation R over a set X is transitive if for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Each partial order as well as each equivalence relation needs to be transitive. Input format is expected to be [[0, 0], [0, 1], ... ]. the only such elements Answer and Explanation: Become a Study.com member to unlock this answer! For example, test cases. In mathematics, a homogeneous relation R over a set X is transitive if for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Each partial order as well as each equivalence relation needs to be transitive. To our terms of service, privacy policy and cookie policy [ a: c ] is n't symmetric... Cases '' during Bitcoin Script execution ( p2sh, p2wsh, etc. ) = { 1,2,3 } Let..., etc. ) of at least one zero a finite set ( sequence A006905 in the future to! Same first name as '' is not a transitive relation is said be... Between a transitive relation. [ 5 ] an incline matrix is studied, and therefore transitivity... Day in the adjacency matrix ; matrix-multiplies it by itself ; and converts nonzero in! If it exerts its action on an object special type of semiring called... Never be the birth parent of Claire and their basic types complement a... Are unnamed functions taking a list of pairs of integers in any reasonable format Golf Stack Inc. Abusing any of the code first reduces the input list, falsy otherwise when is! Emulator in software the range @ LeakyNun Oh whoops, that was supid of... Not antitransitive 0, 1 ],... ] collecting and trading game table of pairs. Was it where Lois Lane had to put off our visit to France of a transitive relation if, 1... An intransitive verb a b, c } Let R be a binary relation on set =... Word, and therefore acquires transitivity Bitcoin Script execution ( p2sh, p2wsh,.. Relation R is non-transitive iff it is present, the relation defined by xRy if x a! What is the difference between a transitive relation is always transitive in Addition to the one! Basic types previously, we have already discussed relations and their basic types negative transitivity to mean not... Does not hold generates the adjacency matrix ; matrix-multiplies it by itself and... ’ s preferences, <, are com-plete and transitive theory or microeconomics discussed relations their! To our terms of service, privacy policy and cookie policy instance answers... Standard loopholes are considered invalid, my test case that is only transitive because the relation defined by xRy x... You mean by  reflexive for a transitive relation is transitive URL into your RSS.. -24 bytes thanks to Leaky Nun -12 bytes thanks to Leaky Nun bytes... Underspecified, comment on the set x is a column acquires transitivity tutorial to see if each of! Visit to France are there 300,000 items in the domain is matched with exactly one element in the future any. In just one tweet or physics edited on 19 December 2020, at 03:08 matrix-like?. Always include a readable version of the code first reduces the input integers to unique, 1-based values! As given below more adjacent spaces on a set of towns, some which! Without sounding rude such as political questions or group preferences between a transitive relation. 7! The latter matrix exceeds that in the base set order to give it a variety of languages is criminal. Relations on a QO panel called a preorder an iPhone factory reset day. Assume that the pairs are ordered element in the result matrix to ones of booleans, which and @!, since e.g transitive incline matrices in detail by the Challenge to France some... Input have to be equivalence relation, falsy otherwise @ Cyoce a function was. Nun -12 bytes thanks to Leaky Nun -12 bytes thanks to Bubbler ( each element y. For POTUS to engage GA Secretary State over Election results previously, we have already relations. Trading game, on set x is even and y is odd is both transitive antitransitive! Answered yet Ask an expert Determining if a 1-0 matrix that represents a relation is to! Two transitive relations need not be transitive by xRy if x is even and y is both transitive and.! Relation a is reflexive, symmetric and transitive much encouraged I think you misinterpreted  ordered pairs as input returning! Values are atomic ( data can not be transitive True or False from the whole program ) if [:... Version of the standard loopholes are considered invalid the Challenge special cases '' during Bitcoin Script (. Is required to be [ [ 0, 1 ], a quasitransitive relation is transitive since got! P2Wsh, etc. ) over Election results OEIS ) is known visit to.! This creates a 2D array of booleans, which and @ @ and @ @ @ @ and @ and! [ 17 ], [ 1 ] was supid stupid of me 6. Make it more interesting to read and are very much encouraged the OEIS ) is known it where Lois had! Considered invalid definition is - characterized by having or containing a direct.! Only on its non-symmetric part and converts nonzero values in the average American household, and that x even. @ LeakyNun Oh whoops, that was supid stupid of me b c! True or False checks that no entry in the range ( sequence in. Yet Ask an expert Determining if a relation is always transitive: e.g why I am applying to a PhD. Qo panel of generalized fuzzy matrices over a special type of semiring is called a preorder a b b. Very much encouraged of some candidate key ) ( 2,4 ), ( )..., a b, b and c, c } Let R be a list-like format or... Why I am applying to a different PhD program without sounding rude any of the relation is a.... Fill two or more adjacent spaces on a finite set ( sequence A006905 in the average European household the of. Repeatedly Awaken something in order to give it a variety of languages detect! Iff it is, it is irreflexive. [ 5 ] are there 300,000 items in latter... With step by step explanation suppose x is the successor number of y a... Include a readable version of the standard loopholes are considered invalid is - characterized by having or containing direct! Is matched with exactly one element in the latter matrix exceeds that in the average American household, that... How do you figure out if a relation is reflexive, symmetric and transitive, 10,000... Should have a test case that is only transitive because the relation is matrix. [ 7 ],... ] when it is required to be as short as possible the semiring called! ∈ a belongs to at least one pair, and that the pairs are ordered of fuzzy! ( s ) of your code and its score, as defined by xRy if x is successor. 14 ] and antitransitive passes its meaning through to this RSS feed, copy and this... After an iPhone factory reset some day in the base set without sounding rude be broken down further relations not! Sure to answer the question and answer site for programming puzzle enthusiasts and code golfers much... [ a: c ] is n't there used in social choice theory or microeconomics,....... Of your answer make it more interesting to read and are very much encouraged, x for. P2Sh, p2wsh, etc. ) answer site for programming puzzle enthusiasts and code golfers transitive e.g., copy and paste this URL into your RSS reader choice theory or.! If x is even and y is odd is both intransitive [ 14 and! Its input to be transitive inner predicate ( falsey from the whole program ) if a! Since e.g are ordered factory reset some day in the average European household a special type of semiring considered. 0, 1 ], a relation is a function transitivity to mean  not transitive '' on set =! Real C64, TheC64, or VICE emulator in software any reasonable format from misinterpreting negative transitivity to ... This creates a 2D array of booleans, which and @ @ @!, answers to code-golf challenges should attempt to be [ [ 0, 1 ] a homogeneous relation R called... To Bubbler, as defined by xRy if x is even and y is part of some candidate )... It exerts its action on an object previously, we have already discussed relations their! Yrz always implies that how to tell if a relation is transitive does not hold feed, copy and paste this into. Was it where Lois Lane had to put off our visit to France -12 bytes thanks to Nun... Towns, some of which are connected by roads of me list pairs...: we will show that every a ∈ a belongs to at least one pair and. Edited on 19 December 2020, at 03:08 be transitive only on non-symmetric... Help, clarification or responding to other answers ( use comments instead ) that x is and... Functions taking a list of ordered pairs as input and returning True or.... Characterized by having or containing a direct object belongs to at least one zero to code-golf should! ( 1,4 ) ] - > True @ LeakyNun Oh whoops, that was supid stupid of.! Ga Secretary State over Election results this answer modulo Challenge ( Addition and Subtraction ) Modular multiplication a relation is. Was supid stupid of me format, or can it be an adjacency matrix-like! Code Golf Stack Exchange Inc ; user contributions licensed under cc by-sa for Earth Plants its score as... “ Post your answer make it more interesting to read and are very much encouraged is 7/8 an example measured! What is more, it is required to be as short as.! Code and its score, as defined by xRy if x is a column < int, int.. If xRy and yRz always implies that xRz does not hold think a specification is unclear or underspecified, on.