# Tagged Questions

For reflexive, symmetric and transitive relations. Use it with the tag (relations).

24 views

### Equivalence Relation Proof Question [duplicate]

Let $R$ be the relation on $N\times (N\setminus\{0\})$ defined by $((a, b),(c, d)) \in R$ if $ad = bc$. Prove that $R$ is an equivalence relation. I'm pretty confused with this problem, mainly ...
28 views

### If a relation is built with $=$, is the relation always an equivalence relation?

$R \subset \Bbb R \times \Bbb R$ I have now encountered a couple of relations that have the following form: $$R=\{(a,b)\in \Bbb R\times \Bbb R\,:\,a^2 = b^2\}$$ They seem to be always equivalence ...
42 views

### Is $R=\{(a,b)\in \Bbb N\times \Bbb N\,:\,(a - b)$ is an odd number $\}$ an equivalence relation?

$R \subset \Bbb N \times \Bbb N$ Is this an equivalence relation? $R=\{(a,b)\in \Bbb N\times \Bbb N\,:\,(a - b)$ is an odd number $\}$ I say it is not because $(a, a)$ is always $0$ which is ...
45 views

### Is the relation $R$ on $\Bbb N$ given by $(a,b)\in R\iff a\mid b$ an equivalence relation?

$R \subset \Bbb N \times \Bbb N$ Is this an equivalence relation? $$R=\{(a,b)\in \Bbb N\times \Bbb N\,:\,a\mid b\}$$ I would argue that it is reflexive because $a\mid a$, but it is not symmetric ...
32 views

257 views

59 views

### Discrete mathematics, equivalence relations, functions.

I'd like some insight on how to 'solve' this problem (more towards understanding what the problem is asking) Suppose that $A$ is a nonempty set and $\mathcal{R}$ is an equivalence relation on $A$...
3k views

25 views

34 views

### Symmetric difference with Identity relation - equivalence relation?

I have the following question and could not find any contradiction.. Let R,S be an equivalence relations on a set A. Determine if $(R\Delta S)∪I_A$ an equivalence relation on set A. ...
52 views

### Circles and generic implicit functions

I have some problems understanding circles. $x^2+y^2 = 1$ is a circle. It defines equivalence class where all (x,y) points belonging to the circle are in the same equivalence class. $(\cos a, \sin a)$...
50 views

### Can a simple (atomic) proposition be a tautology?

Definition: "A tautology is a propositional formula that is true under any truth assignment to each of the atomic propositions in the domain of propositional function." Let $p$ be a simple (or atomic)...
19 views

### Proportionality between two quantities

Its known that if one variable is proportional to two others than it is also proportional to their product. $$\forall a,b,c\in ℝ:a\propto b\wedge a\propto c\Rightarrow a\propto b\cdot c$$ I think i`ve ...
33 views

### Prove that this is an Equivalence Relation.

Then give information about the equivalence classes as specified for The relation $R$ on $ℝ$ given by $xRy$ iff $x-y∈ℚ$. Give the equivalence class of $0$; of $1$ ; $\sqrt{2}$. First In order to ...
16 views

33 views

### what is the complete set of representatives of an equivalence class?

I have been researching the topic, but I can't find anything that explains specifically and in detail what it is. I just find a bunch of exercises about the topic.
22 views

43 views

### An uncountable chain of equivalence relations

First, an example: We know that, for two real valued, Lebesgue-integrable functions, the relation "equals almost everywhere" is an equivalence relation. In particular, if $f_0$ is Lebesgue-integrable, ...
Let $A$ = {$a,b,c$}. Give an example of a relation on $A$ that is anti-symmetric, reflexive on $A$ and symmetric. The first thing that one must do to proceed with this question is to first define ...
There are many different equivalence relation possible on the set $A = \{a, b, c, d\}.$ For example, here are just two different ones: (a) \$E_1 = \{(a, a), (b, b), (c, c), (d, d), (a, c), (c, a), (b, ...