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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A question on relations

Problem Statement: Let $A$ and $B$ be sets. Many books define a relation $\mathcal R$ from $A$ to $B$ to be a subset $ \mathcal R \subseteq A \times B $. Show that such an R is a ...
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Two functions whose order can't be equated - big O notation

Our teacher talked today in the class about big O notation, and about order relations. she mentioned that the set of order of magnitude, is not linear Meaning, there are function $f,g$ such that $f$ ...
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What would make a function reflexive, transitive, and/or symmetric?

A binary relation $R$ is a subset of the Cartesian product between two sets $X$ and $Y$, containing a set of ordered pairs $\{(x,y) : x \in X, y \in Y\}$. $R$ is a function if each element of $X$ is ...
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How many reflexive binary relations there are on a finite countable set?

We know that binary relation is subset of Cartesian product made by set on to itself. let's say we have a set with two elements $A=\{0,1\}$ So Cartesian product is $C=A\times A = ...
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2answers
57 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
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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 ...
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28 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 ...
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1answer
50 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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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
27 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 ...
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3answers
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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 ...
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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: $$R = \{(x, y)\mid xy = 12\}$$ $$S = \{(x, y)\mid 2x = 3y\}$$ ...
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1answer
24 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 ...
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1answer
32 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 ...
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1answer
36 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 ...
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45 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 ...
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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 ...
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1answer
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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 ...
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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, ...
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How to tell if relation is symetric, reflexive, or transitive? [closed]

Is the following relation transitive, reflexive ,or symmetric. R where where $(x,y)R(z,w)$ if and only if $x+z\le y+w$ on the set real number Cartesian product real number.
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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 ...
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1answer
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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.
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Finding the composition of relation?

Let $R=\{(1,5),(2,2),(3,4),(5,2)\}$ $S=\{(2,4),(3,4),(3,1),(5,5)\}$ $T=\{(1,4),(3,5),(4,1)\}$ 1.Find $R$ composite $T$ 2. Find $R$ composite $R$ 3. Find $T$ composite $T$ For all these I made a ...
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1answer
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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...
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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.
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1answer
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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
114 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 ...
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3answers
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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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1answer
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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 $10\times3$ ...
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73 views

How can we prove these equivalence relations [closed]

We have this relation $A= (\mathbb Z_{\geq0})\times(\mathbb Z_{\geq0})\times\ldots\times(\mathbb Z_{\geq0})$. And we have the relation $R$ on $A$ such that: $(a , b)R(c , d)\iff a+d=c+b$ and ...
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107 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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“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 ...
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1answer
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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
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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
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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": $\forall a, b \left< ...
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1answer
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$\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
43 views

Blood relation - How A is related to B

This is a data sufficiency question - Q - How is A related to B? ...
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1answer
26 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 ...
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For which sets, $X$ the relation is a partial function

Given $T=\left\{\ \left<A,B\right> \in (P(X))^2 | A\subseteq B \right\}$ For which sets, $X$, the relation $(P(X))^2-T \cap (P(X))^2-T^{-1}$ is a partial function? Here's my solution: ...
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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 ...
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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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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), ...
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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 ...
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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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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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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 ...
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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
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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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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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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 ...