# Tagged Questions

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### 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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### Equivalence relation question with cardinality and countability $A=\mathbb R,\ aSb \iff a-b\in \mathbb Q$

Let $A=\mathbb R,\ aSb \iff a-b\in \mathbb Q$ What is the cardinality of $[\pi]_S$ ? Prove that the quotient group $\mathbb R/S$ is uncountable. Well I think that cardinality is ...
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### Prove or disprove question with equivalence relation, classes and quotient group

Let $A$ be a set and $R$ an equivalence relation on $A$. Prove or disprove: If $A$ is countable then all the equivalence classes of $R$ are countable. If $A$ isn't countable then the ...
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### Equivalence relation question with functions

We'll define on the set: $A=\Bbb R^{[0,1]}$ the relation $R$ by $fRg$ if $f(0)=g(0)$. Make sure it's an equivilence relation. What is $[\cos x]$ ? Describe all the equivalence classes ...
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### Proof of equivalence relation on a set

Let $X = \{(a,b) \mid a,b \in \Bbb Z; b \ne 0\}$. We define $(a,b)\mathrel R (c,d)$ iff $ad = bc$. Prove that $R$ is an equivalence relation on the set $X$. Which known set do the equivalence classes ...
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### Properties of the relation $R=A\times B \cup B\times A$

A is a set. Let $B\subsetneq A$. $R=A\times B \cup B\times A$ Determine if the relation is (a)reflexive, (b)symmetric, (c)transitive, (d)anti-reflexive, (e)anti-symmetric, (f)asymmetric, ...
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### Properties of the relation $R=\{(x,y)\in\Bbb R^2|x-y\in \Bbb Z\}$

$A= \Bbb R \\ R=\{(x,y)\in\Bbb R^2|x-y\in \Bbb Z\}$ Determine if the relation is (a)reflexive, (b)symmetric, (c)transitive, (d)anti-reflexive, (e)anti-symmetric, (f)asymmetric, (g)equivalence ...
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### Define a relation on the set of all real numbers $x,y \in \mathbb{R}$ as follows:

Define a relation on the set of all real numbers $x,y \in \Bbb{R}$ as follows: $x \sim y$ if and only if $x - y \in \Bbb{Z}$ Prove this is an equivalence relation and find the equivalence class of ...
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### Is this relation reflexive, symmetric and transitive?

Define a relation $R$ on the set of functions from $\mathbb{R}$ to $\mathbb{R}$ as follows: $(f, g) \in R$ if and only if $f(x) - g(x) \geq 0$ for all $x \in \mathbb{R}$ Is this relation ...
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### Relation symmetric confusion

So Symmetric = (a,b), (b,a) Set = {<1, 1>, <1, 2>, <1, 4>, <2, 1>, <2, 2>, <3, 3>, <4,1 >, <4, 4>} I understand ...
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### Difference between Reflexive and Symmetric in Discrete Maths

Difference between Reflexive and Symmetric in Discrete Maths? This is what I understand: Reflexive -> <a,a=a>, <b,b=b> uses ...
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### Equivalence Classes of a Relation Given as a Set of Ordered Pairs

Question: The relation R is an equivalence relation on the set A. Find the distinct equivalence classes of R. A = {a, b, c, d} R = {(a, a), (b, b), (b, d), (c, c), (d, b), (d, d)} My work: So when ...
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### Reflexive, Symmetric, Anti-Symmetric relations

Let $A = \mathbb Z \times ( \mathbb Z\setminus {0} )$. A binary relation $R$ on $A$ is defined as follows: For all $(a,b),(c,d) \in A$ $$(a,b) \,R\,(c,d) \iff ad = bc$$ now how do I find if $R$ is ...
Let $A=\{1,2,3,4\}$. Let $F$ be the set of all functions from $A$ to $A$. Let $R$ be the relation on $F$ defined by $f,g \in F$ $f R g \Leftrightarrow |f(A)|=|g(A)|$ $f(A)=\{f(x): x\in A\}$ ...