Question

How do I show that the relation $R : \mathbb{Q} \times \mathbb{Q} → \mathbb{Q}$ defined by $R((a/b, c/d)) = ((a+c) / (b+d))$ is not a function?

score 76 · Answer 1 · 2016-12-07 15:02:36

How do I show that the relation $R : \mathbb{Q} \times \mathbb{Q} → \mathbb{Q}$ defined by $R((a/b, c/d)) = ((a+c) / (b+d))$ is not a function?

score 795 · Answer 2 · 2016-12-08 05:30:53

795

Views

What are the relation properties of = {(, ) | gcd(, ) = 1}

Published on 08 Dec 2016 - 5:30

score 28 · Answer 3 · 2026-04-01 22:39:03

28

Views

Let (A, $\preceq$) be a poset.Define a map $f:A \to P(A)$ by $f(x) = \{ y \in A | y \preceq x \}$ for all $x \in A$.

Published on 01 Apr 2026 - 22:39

score 473 · Answer 4 · 2016-12-08 15:23:24

473

Views

How can a set with only two elements have 8 symmetric relations?

Published on 08 Dec 2016 - 15:23

score 116 · Answer 5 · 2026-03-29 12:40:34

116

Views

How to notate that a predicate holds for all elements in a set.

Published on 29 Mar 2026 - 12:40

score 983 · Answer 6 · 2016-12-11 12:27:26

983

Views

Does the definition for transitive relation require distinct values?

Published on 11 Dec 2016 - 12:27

score 278 · Answer 7 · 2026-04-01 22:41:49

278

Views

How do I find the equivalence class of 0? I already wrote the proof.

Published on 01 Apr 2026 - 22:41

score 1.1k · Answer 8 · 2026-04-01 22:37:23

1.1k

Views

The relation A defined on $\mathbb{R}$ by $ \exists k \in \mathbb{Z} , xAy \iff x - y = 2k$ is an equivalence relation.

Published on 01 Apr 2026 - 22:37

score 129 · Answer 9 · 2026-04-01 04:27:07

129

Views

Partial order in $\mathbb R$; supremum; largest; smallest

Published on 01 Apr 2026 - 4:27

score 57 · Answer 10 · 2016-12-13 11:03:10

57

Views

Clarification on a Theorem on Relations(very basic and trival)

Published on 13 Dec 2016 - 11:03

score 2k · Answer 11 · 2026-03-22 00:55:58

2k

Views

Is this Hasse Diagram correct?

Published on 22 Mar 2026 - 0:55

score 1k · Answer 12 · 2026-04-01 22:38:50

1k

Views

Let R be the relation defined on the set of real numbers by xRy iff x=y or xy=1

Published on 01 Apr 2026 - 22:38

score 5k · Answer 13 · 2016-12-13 22:03:16

5k

Views

Prove or Disprove, if R and S are partial order relations on a set A, then $R \cup S$ is a partial order relation on A

Published on 13 Dec 2016 - 22:03

score 640 · Answer 14 · 2026-04-02 00:11:19

640

Views

Equivalence Relation...

Published on 02 Apr 2026 - 0:11

score 110 · Answer 15 · 2016-12-14 03:37:19

110

Views

Properties of relations (symmetry and anti-symmetry)

Published on 14 Dec 2016 - 3:37

List Question

How do I show that the relation $R : \mathbb{Q} \times \mathbb{Q} → \mathbb{Q}$ defined by $R((a/b, c/d)) = ((a+c) / (b+d))$ is not a function?

What are the relation properties of = {(, ) | gcd(, ) = 1}

Let (A, $\preceq$) be a poset.Define a map $f:A \to P(A)$ by $f(x) = \{ y \in A | y \preceq x \}$ for all $x \in A$.

How can a set with only two elements have 8 symmetric relations?

How to notate that a predicate holds for all elements in a set.

Does the definition for transitive relation require distinct values?

How do I find the equivalence class of 0? I already wrote the proof.

The relation A defined on $\mathbb{R}$ by $ \exists k \in \mathbb{Z} , xAy \iff x - y = 2k$ is an equivalence relation.

Partial order in $\mathbb R$; supremum; largest; smallest

Clarification on a Theorem on Relations(very basic and trival)

Is this Hasse Diagram correct?

Let R be the relation defined on the set of real numbers by xRy iff x=y or xy=1

Prove or Disprove, if R and S are partial order relations on a set A, then $R \cup S$ is a partial order relation on A

Equivalence Relation...

Properties of relations (symmetry and anti-symmetry)

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