This tag is intended for questions concerning partial orders, equivalence relations, properties of relations (transitive, symmetric,...), composition of relations and similar stuff. More-or-less the things about relations taught in the first elementary set theory or discrete math course.

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2answers
544 views

Binary relation, reflexive, symmetric and transitive

I have a question regarding an image. I'm currently studying binary relations and the following image confused me: What got me confused is that the page from which I got the link ...
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0answers
39 views

A partial order with more properties than would be expected

Consider the relation: $$\langle x_1,x_2\rangle\prec\langle y_1,y_2\rangle\iff x_1,x_2,y_1,y_2\in\Bbb N\wedge x_1y_2<x_2y_1.$$ This is usually used for defining the (positive) fractions $\Bbb ...
0
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1answer
31 views

New way of combining information in graphs

So, I am working for a social project involving graph theory. I have a dynamic dataset (weighted and undirected), I made graphs out of them ( for 10 years ). Now, I am trying to find out relations ...
0
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1answer
184 views

Understanding the difference between relations and functions.

$R=\{(1,2),(1,3)\}$ is a relation but not function. The logic for this is that if the first element of every ordered pair must remain different, then it is said to be function. Otherwise, it's just ...
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2answers
55 views

Sets and Relations in Math

I have not knowledge about relations, could you help me to solve this excercise step by step, to use in futures excercices? Thanks for your time. Given the set $A = \{1, 2, 3, 4\}$ and $B = \{1, 3, ...
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0answers
35 views

Produce a list of the most-similar units, given various correlations/relationships

I have a database full of units (U1 - U50, U51...) where every unit has the same standard attributes (A1 - A10) and where a % of each attribute defines the amount of that attribute for that particular ...
2
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3answers
46 views

let A be a set of 6 distinct postive integers each <= 12, show that the sum of non empty subests of A cannot all be distinct [closed]

let A be a set of 6 distinct postive integers each <= 12, show that the sum of non empty subsets of A cannot all be distinct. for when does this not continue to hold up ( ie instead of 12 , its ...
1
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1answer
30 views

Relations - Logical Boolean Matrix

I am having trouble with the following question: Relations $S$ and $R$ are defined on the set $$\{1, 2, 3, \ldots, 12\}$$ as follows: $$R = \{(x, y)\mid xy = 12\}$$ $$S = \{(x, y)\mid 2x = 3y\}$$ ...
0
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1answer
37 views

Relations - Ordered Pairs

I have the following question: Relations $S$ and $R$ are defined on the set $$\{1, 2, 3, \ldots, 12\}$$ as follows: $$R = \{(x, y)\mid xy = 12\}$$ $$S = \{(x, y)\mid 2x = 3y\}$$ Write the ordered ...
1
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1answer
124 views

Describing a partition for an equivalence relation?

Describe the partiton for the equivalence relation. For each $x,y\in \mathbb{R}$ xRy $\iff$ $x-y\in \mathbb{Z}$ Now I am not sure how to find a partition for this I guess one could have negative ...
0
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1answer
37 views

showing if $ x\equiv_my\rightarrow\frac{x}{r}=\frac{y}{r}$

How would I show this proposition. $ x\equiv_my\rightarrow\frac{x}{r}=\frac{y}{r}$ I will make $\frac{x}{r}$ capital X because it is easier to write. And $\frac{y}{r}$ capital Y. These are the ...
0
votes
3answers
378 views

Giving an equivalence relation that corresponds to set partitions

My question is: Give equivalence relation that corresponds to the partitions A1 = {1,3,5} A2 = {2} A3 = {4,6} of the set A = {1,2,3,4,5,6} I don't know what the format of the relation should be, in ...
0
votes
3answers
358 views

Showing $ x-y\in\mathbb{Q}$ is an equivalence relation?

How would one show the the following is an equivalence relation. The relation R on the real numbers given by xRy iff number $ x-y\in\mathbb{Q}$. This is what I did. Reflexive Let $x \in ...
1
vote
1answer
46 views

Finding the cardinality of $\{X\in \mathcal P(\mathbb R)| |X|=\aleph_0 \}$

Let $S$ be a relation over $\mathcal P(\mathbb R)$ such that $A,B\subseteq\mathbb R: \exists f:A\to B, \exists g: B\to A$ and $f,g$ are injections. Find the cardinality of $\{X\in \mathcal ...
3
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5answers
3k views

Real life examples of order relations.

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, ...
2
votes
3answers
89 views

Name for relationship where a is related to b iff a and b are in different subsets

Yesterday I was out running in the park, and like many others I always run in a counterclockwise direction around the central lake. There are also strange people who always run in a clockwise ...
0
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1answer
40 views

Define a numeric relation that is reflexive, but not symmetric or transitive.

Define a numeric relation that is reflexive, but not symmetric or transitive. I've googled on this one quite a bit and am stuck.
-1
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1answer
82 views

Showing a counter example $(A\times B)\times C=A\times (B\times C)$

Showing a counter example $(A\times B)\times C=A\times (B\times C)$ I think $A=\{1\}$ $B=\{2\}=C$ Would work but I am not sure...
7
votes
10answers
3k views

I need a relation which is not reflexive, not symmetric, and not transitive

I need an example of a relation which is simultaneously not reflexive, not symmetric, and not transitive. Any accessible examples? Thanks in advance.
1
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1answer
56 views

Showing $ (R ∪ R^{-1})^∗ = R^∗ ∪ R^{−1∗} $ is false by giving a counterexample.

Show that $$ (R ∪ R^{-1})^∗ = R^∗ ∪ R^{−1∗} $$ is false by giving a counterexample. I tried the following, but every time it keeps coming out as true (instead of false): If $R = \{(a,b), ...
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2answers
122 views

How would I go about solving this question on derivatives?

The base of a $13-ft$ ladder that is leaning against a wall begins to slide away from the wall. When the base is 12 ft from the wall and moving at the rate of $3 ft/sec$, how fast is the top of the ...
2
votes
3answers
295 views

Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
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2answers
38 views

Showing $(a,b) \sim (c,d)$ iff $a+d=b+c$ is transitive on $\mathbb{N}$

I am given: $a,b,c,d \in \mathbb{N}$, $a \neq c$, and $b \neq d$. The relation $\sim$ on $\mathbb{N}\times\mathbb{N}$ is defined by $(a, b) \sim (c, d)$ iff $a+d=b+c$ for all $(a,b), (c,d) \in ...
3
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1answer
94 views

Is taking the Euclidean norm of multiple Euclidean norms equivalent to taking the Frobenius norm?

I'm just a programmer venturing into the world of norms (is that even a thing?) here, and am wondering if two formulas are equivalent. Please forgive my ignorance! Suppose we have a $10\times3$ ...
0
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0answers
143 views

preference relation.

In the exercise below I need to check whether the relation below is a preference relation ( need to be transitive (if $x>y$ and $y>z$ then $x>z$) and connected ). But I cannot find an ...
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2answers
60 views

“Simple” math question about length and rotation relations

I'm currently building a robot arm as a hobby, and I'm still in the planning phase. But I've encountered a small problem, where my knowledge doesn't suffice. This is what I am trying to achieve: I ...
1
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1answer
26 views

Name for the type of relation similar to the edge set of a regular directed graph?

For a binary relation over a set, if each member in the set appears the same number of times in the first position and in the second position in the relation, is there a name for such a relation? For ...
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2answers
541 views

Relations on a set, check my answers?

I've been struggling with identifying relations on a set, and was hoping someone could check my answers and make sure I'm on the right track. Let A = {1,2,3,4} and R be a relation on the set A ...
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1answer
90 views

Antisymmetric relation (“strong” vs “weak”)

Defining: "weak antisymmetric relation": $\forall a, b \left< a,b \right> \in R \land \left< b,a \right> \in R \Rightarrow a=b$ "Strong antisymmetric relation": $\forall a, b \left< ...
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1answer
48 views

$\sum_{x=a}^{b-1}\frac{1}{x}$ and $\sum_{x=a+1}^b\frac{1}{x}$

I have to prove the following relations: $\sum_{x=a}^{b-1}\frac{1}{x}\geq\log b - \log a $ $\sum_{x=a+1}^{b}\frac{1}{x}\leq\log b - \log a $ I tried to use the relation that $\int_a^b \frac{1}{x} ...
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1answer
138 views

Blood relation - How A is related to B

This is a data sufficiency question - Q - How is A related to B? ...
1
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1answer
43 views

Name for a generalized relation to be a multiset?

A relation between two sets $A$ and $B$ is a subset of $A \times B$. If taking a multiset subset of $A \times B$, e.g. allowing $(a,b)$ appears twice in the subset, is there a name for such a ...
3
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0answers
40 views

Divisibilty as relation set on $(\mathbb N \setminus \{0,1\})$

So i have to see if $\prec$ is order relation where two elements $(a,b)$ and $(c,d)$ are in relation $\prec$ if $a|c$ and $2b^{2}+6b\leq2d^{2} + 6 d$. This relation is defined on set $(\mathbb N ...
2
votes
1answer
276 views

Is the property reflexive, symmetric, anti-symmetric, transitive, equivalence relation, partially ordered given the relation below?

I'm working on this and I'm supposed to figure out if the following properties apply to the below relations. Properties are: ...
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1answer
35 views

Relation theory

Let S be a set and R a relation on that set. A subset T of S is said to be a right R-set if it is of the form {x|sRx} for some constant s in S. The collection of all right R-sets is a subset of P(S), ...
0
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2answers
95 views

Greatest lower and least upper bounds for a set of pairs

Had some trouble with this question in an exam recently, and wanted to make sure I reasoned correctly. The question was: $X$ is a set of pairs of real numbers $(x,y)$, with absolute values less than ...
0
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1answer
42 views

How do I derive a contradiction from an assumption that is “not asymmetric”

Let $R$ be a transitive relation on a set $A$. Define another relation, $S$, such that, for any $x,y \in A$, $Sxy$ iff $Ryx$. Moreover, let $S$ be irreflexive. Prove: $S$ is asymmetric on $A$. ...
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0answers
101 views

Using the ELO Rating System on Static Objects

The Setup Suppose we have a list of movies $m_1, m_2, \dots, m_n$ that we wish to rank in order of "quality." We define the "strength" of a movie $a$ by a function $f$ which takes in numerical ...
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2answers
60 views

Find the $f(x)$ from the given information

So tomorrow I tackled a maths test where I faced a question which was saying, Question: Let $f:R-\{0,1\}\rightarrow R$ be a function satisfying the relation ...
0
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2answers
368 views

Finding the equivalence classes of a trigonometric relation

I have been asked to respond to the following: Define a binary relation R on $\mathbb{R}$ as ${\{(x, y) \in \mathbb{R} \times \mathbb{R} \mid \sin(x) = \sin(y)\}}$. Prove that R is an ...
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1answer
48 views

Domain of definition of the function

I was going through some questions of Relations and Functions and now I am stuck to one. Question says Question: Domain of definition of the function $$f(x)=\frac{9}{9-x^2}+\log_{10}(x^3-x)$$ ...
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0answers
143 views

Have you seen this property of tolerance relations before?

Let $A$ be a set equipped with a binary reflexive and symmetric relation $\uparrow$ (such relations are often called tolerances, see also "Are there real-life relations which are symmetric and ...
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1answer
19 views

Common numbers in sequences

Lets say we have a set $S$ of $N$ ($N\geq 3$) finite nonempty sequences of numbers, each of different length. Is the relation of "having some number or numbers in common" transitive on $S$? I have no ...
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2answers
200 views

Reflexive/Symmetric/Antisymmetric/Transitive

I am having issues identifying if the following are reflexive/symmetric/antisymmetric/transitive. Could anybody help me out? I have the book definitions but I'm confused on really the application of ...
1
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1answer
119 views

relation r reflexivity, transitivity, symmetry

check if relation r is reflexivity, transitivity, symmetry. r is a binary relation in the set of natural numbers such that x r y (x mod 3) = (y+1 mod 3). x-y-1≡(3 mod) <=>x-y-1=3k, for some k ∈ ...
0
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1answer
77 views

What's the difference between a partial function and a relation?

My understanding of a partial function is that it is one which only maps a subset of some set $A$ to another set $B$ (where $B$ could be $A$). On the Wikipedia page, the below image is given as an ...
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1answer
23 views

Value assignment for complete, transitive relation on uncountably infinite set

Consider a set $A$ and a relation $r$. The relation $r$ is complete, i.e., for any $a,b\in A$, we have $arb$ or $bra$ or both. The relation $r$ is transitive, i.e., for any $a,b,c\in A$, if $arb$ ...
2
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1answer
32 views

Value assignment for complete, transitive relation on countably infinite set

Consider a set $A$ and a relation $r$. The relation $r$ is complete, i.e., for any $a,b\in A$, we have $arb$ or $bra$ or both. The relation $r$ is transitive, i.e., for any $a,b,c\in A$, if $arb$ ...
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2answers
53 views

Value assignment for complete, transitive relation

Consider a finite set $A$ and a relation $r$. The relation $r$ is complete, i.e., for any $a,b\in A$, we have $arb$ or $bra$ or both. The relation $r$ is transitive, i.e., for any $a,b,c\in A$, if ...
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0answers
90 views

Prove/disprove questions on equivalence relations and ordered sets

If $R$ is an equivalence relation and a partial order over $A \neq \emptyset$ then every equivalence class contain at least one element. If $(A,\le)$ an ordered set, and $a\in A$ is a single ...