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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2
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2answers
52 views

What is it called when !(a < b) and !(b < a) implies a = b?

I thought it would be some kind of symmetric equality but its impossible to do a google search on this, all I get are definitions of reflexive, symmetric and transitive. I'm not really sure which ...
1
vote
1answer
14 views

Equivalence between different definitions of transitive closure

Let $W$ be an arbitrary, non-empty set and let $R$ be an arbitrary binary relation on $W$. Define the transitive closure of $R$ as $R^+ = \bigcap \{ R' \; | \; R' \text{ is a binary transitive ...
2
votes
1answer
37 views

Relations and functions with valence 0

From http://en.wikipedia.org/wiki/First-order_logic#Non-logical_symbols Relations of valence 0 can be identified with propositional variables. For example, P, which can stand for any ...
3
votes
3answers
37 views

An example of symmetric transitive relation that is not reflexive on a set of natural numbers $\mathbb{N}$ [duplicate]

An example of symmetric transitive relation that is not reflexive on a set of natural numbers $\mathbb{N}$. My guess is that such relation does not exist, but I don't know how to prove it.
1
vote
2answers
33 views

What is the name of the Speed, Distance, Time relationship?

Really simply, I'd like to know if there is a name used to describe the speed, distance & time relationship. i.e. As this is basically the same relationship that applies to current, voltage and ...
0
votes
1answer
35 views

How many relations exist in the set of A

When A = {1,b,ø}, how many reflexive relations exist on the set? I have said that AxA={(1,1), (b,b), (ø,ø), (1,b), (1,ø), (b,1), (b,ø), (ø,1), (ø,b)} Would I be right in saying that there are only 3 ...
0
votes
0answers
25 views

Is this connected relation?

My task is to check if this is preference relation (connected and transitivited) $$ f \succeq g \Leftrightarrow \forall x\in [0,1] f'(x) \leq g'(x) $$ My solution is: that this relation is not ...
1
vote
1answer
30 views

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 ...
5
votes
2answers
28 views

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 $f$ ...
0
votes
3answers
58 views

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 ...
1
vote
3answers
20 views

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 = ...
2
votes
2answers
49 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 ...
1
vote
0answers
29 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
votes
1answer
27 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
votes
1answer
39 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 ...
0
votes
2answers
51 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, ...
0
votes
0answers
16 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
votes
3answers
36 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 ...
0
votes
1answer
15 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
votes
1answer
23 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
vote
1answer
31 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
votes
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 ...
0
votes
3answers
36 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
56 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
28 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
votes
5answers
294 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
2answers
46 views

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.
2
votes
3answers
59 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
votes
1answer
23 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.
0
votes
0answers
28 views

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 ...
-1
votes
1answer
71 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...
6
votes
10answers
2k 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
vote
1answer
54 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), ...
1
vote
2answers
112 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
66 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 ...
3
votes
1answer
28 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
votes
1answer
71 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 ...
0
votes
0answers
103 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 ...
1
vote
2answers
33 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
vote
1answer
19 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 ...
1
vote
2answers
22 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 ...
1
vote
1answer
17 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< ...
1
vote
1answer
45 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} ...
0
votes
1answer
42 views

Blood relation - How A is related to B

This is a data sufficiency question - Q - How is A related to B? ...
1
vote
1answer
23 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 ...
0
votes
0answers
10 views

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: ...
3
votes
0answers
33 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 ...
1
vote
1answer
29 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: ...
0
votes
1answer
21 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
28 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 ...