Question

Prove or disprove: if $R$ and $S$ are two equivalence relations on a set $A$ then $R\cup S$ is also an equivalence relation.

score 10.4k · Answer 1 · 2016-10-03 17:27:56

10.4k

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Prove or disprove: if $R$ and $S$ are two equivalence relations on a set $A$ then $R\cup S$ is also an equivalence relation.

Published on 03 Oct 2016 - 17:27

score 124 · Answer 2 · 2016-10-03 18:55:14

124

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A question on a proof of the existence of non-measurable sets

Published on 03 Oct 2016 - 18:55

score 25 · Answer 3 · 2016-10-04 10:40:57

25

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Showing that $A^T_p$ is similar to $A_p$

Published on 04 Oct 2016 - 10:40

score 63 · Answer 4 · 2016-10-05 08:07:18

63

Views

Prove that a given "multiplication" operation on $\mathbb{N} \times \mathbb{N}$ respects a given equivalance relation?

Published on 05 Oct 2016 - 8:07

score 636 · Answer 5 · 2016-10-05 18:05:42

636

Views

Let R and S are "Congruence modulo 4" and "Congruence modul0 6" relations respectively on set of integers, R={(a,b)| a=b(mod 4), S={(a,b)| a=b(mod 6)

Published on 05 Oct 2016 - 18:05

score 146 · Answer 6 · 2026-03-27 07:31:10

146

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Proof Help: Let $R$ be an equivalence relation on $A$. And, let $x, y, z \in A$. If $x \in y/R$ and $z \not \in x/R$, then $z \not \in y/R$.

Published on 27 Mar 2026 - 7:31

score 427 · Answer 7 · 2026-03-27 07:36:31

427

Views

Get size of relation |R|

Published on 27 Mar 2026 - 7:36

score 132 · Answer 8 · 2026-03-25 10:56:53

132

Views

Prove $[a],[b]\in\mathbb{Z}$ and $[a]=[a']$ and $[b]=[b']$ imply $[a]+[b]=[a+b]=[a'+b']=[a']+[b']$

Published on 25 Mar 2026 - 10:56

score 176 · Answer 9 · 2026-03-27 07:37:20

176

Views

Equivalence Relation on $(\mathbb{R} - \{0\}) \times \mathbb{R}$ defined by $(x, y) \sim (u, v) \iff xv=yu$

Published on 27 Mar 2026 - 7:37

score 29 · Answer 10 · 2016-10-07 01:25:19

29

Views

Seeing if a relation on set Z is a equivalence relation

Published on 07 Oct 2016 - 1:25

score 83 · Answer 11 · 2016-10-07 17:36:17

83

Views

Equivalence relation notation

Published on 07 Oct 2016 - 17:36

score 410 · Answer 12 · 2016-10-10 00:09:09

410

Views

Confused on equivalence relationships with the equation $y=x^2$

Published on 10 Oct 2016 - 0:09

score 90 · Answer 13 · 2016-10-11 18:45:30

90

Views

Is this relation an equivalence?

Published on 11 Oct 2016 - 18:45

score 26 · Answer 14 · 2016-10-12 01:18:59

26

Views

Prove transitivity of relation $R=\{(a,b) \in Z \times Z | \exists m,n \in N\setminus\{0\}: a^m = b^n \}$

Published on 12 Oct 2016 - 1:18

score 986 · Answer 15 · 2016-10-12 23:59:55

986

Views

Need help with proving equivalence relation on Z x Z

Published on 12 Oct 2016 - 23:59

List Question

Prove or disprove: if $R$ and $S$ are two equivalence relations on a set $A$ then $R\cup S$ is also an equivalence relation.

A question on a proof of the existence of non-measurable sets

Showing that $A^T_p$ is similar to $A_p$

Prove that a given "multiplication" operation on $\mathbb{N} \times \mathbb{N}$ respects a given equivalance relation?

Let R and S are "Congruence modulo 4" and "Congruence modul0 6" relations respectively on set of integers, R={(a,b)| a=b(mod 4), S={(a,b)| a=b(mod 6)

Proof Help: Let $R$ be an equivalence relation on $A$. And, let $x, y, z \in A$. If $x \in y/R$ and $z \not \in x/R$, then $z \not \in y/R$.

Get size of relation |R|

Prove $[a],[b]\in\mathbb{Z}$ and $[a]=[a']$ and $[b]=[b']$ imply $[a]+[b]=[a+b]=[a'+b']=[a']+[b']$

Equivalence Relation on $(\mathbb{R} - \{0\}) \times \mathbb{R}$ defined by $(x, y) \sim (u, v) \iff xv=yu$

Seeing if a relation on set Z is a equivalence relation

Equivalence relation notation

Confused on equivalence relationships with the equation $y=x^2$

Is this relation an equivalence?

Prove transitivity of relation $R=\{(a,b) \in Z \times Z | \exists m,n \in N\setminus\{0\}: a^m = b^n \}$

Need help with proving equivalence relation on Z x Z

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