List questions from equivalence-relations

Published on 07 Apr 2026 - 18:54

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Define a relation $ \sim$ on $\mathbb{R}^2 \setminus (0,0)$ by $(a,b)\sim (c,d)$ if there is some real number x with $a=xc$ and $b=xd$.

Published on 31 Aug 2017 - 16:58

412

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Testing whether "$\emptyset$ in $ \emptyset$ " is an equivalence relation

Published on 31 Aug 2017 - 17:37

9.6k

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How do I describe the equivalence classes in $\mathbf{R}$ of the relation $x\mathsf{R}y$ if $x - y \in \mathbf{Z}$?

Published on 02 Sep 2017 - 15:18

1.8k

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Proving $S$ is an equivalence relation and R⊆S

Published on 05 Sep 2017 - 22:18

1.6k

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How to find the distinct equivalence classes for the set of all bit strings of length 5

Published on 23 Feb 2026 - 15:26

66

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Suppose that $(a_1, b_1) + (c_1, d_1) = (a_1d_1 + b_1c_1, b_1d_1)$. Prove this addition is well-defined.

Published on 13 Sep 2017 - 8:45

160

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Multiplication of sequences and equivalence relations

Published on 07 Apr 2026 - 18:08

237

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Is this an equivalence relation on $A$?

Published on 14 Sep 2017 - 1:31

576

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Quotient Map of the Torus is Not Open

Published on 26 Mar 2026 - 19:01

87

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How to show that the following relation is transitive (What is the idea?)

Published on 14 Sep 2017 - 2:38

356

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How to prove substitution from properties of equivalence relations?

Published on 01 Apr 2026 - 16:23

1.8k

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R is symmetric and transitive relation, if and only if $R = R^{-1}\circ R$

Published on 30 Mar 2026 - 14:43

126

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Equivalence Rules Proofs

Published on 25 Mar 2026 - 11:08

224

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Bourbaki exercise on intransitive relations

Published on 20 Sep 2017 - 0:43

List Question

Proof $[h]_r$ is infinite countable.

Define a relation $ \sim$ on $\mathbb{R}^2 \setminus (0,0)$ by $(a,b)\sim (c,d)$ if there is some real number x with $a=xc$ and $b=xd$.

Testing whether "$\emptyset$ in $ \emptyset$ " is an equivalence relation

How do I describe the equivalence classes in $\mathbf{R}$ of the relation $x\mathsf{R}y$ if $x - y \in \mathbf{Z}$?

Proving $S$ is an equivalence relation and R⊆S

How to find the distinct equivalence classes for the set of all bit strings of length 5

Suppose that $(a_1, b_1) + (c_1, d_1) = (a_1d_1 + b_1c_1, b_1d_1)$. Prove this addition is well-defined.

Multiplication of sequences and equivalence relations

Is this an equivalence relation on $A$?

Quotient Map of the Torus is Not Open

How to show that the following relation is transitive (What is the idea?)

How to prove substitution from properties of equivalence relations?

R is symmetric and transitive relation, if and only if $R = R^{-1}\circ R$

Equivalence Rules Proofs

Bourbaki exercise on intransitive relations

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