Question

How is it possible to have a transitive yet not complete relation?

score 8k · Answer 1 · 2026-04-08 16:47:23

8k

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How is it possible to have a transitive yet not complete relation?

Published on 08 Apr 2026 - 16:47

score 770 · Answer 2 · 2013-11-03 11:25:58

770

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Proving that $R$ is antisymmetric if and only if $G \cap G^{-1} \subseteq D$

Published on 03 Nov 2013 - 11:25

score 211 · Answer 3 · 2013-11-03 22:36:08

211

Views

Proving that $aRb \iff a = b \lor a = b^2$ is antisymmetric.

Published on 03 Nov 2013 - 22:36

score 133 · Answer 4 · 2013-11-04 02:00:44

133

Views

How can I further simplify $(a \le b) \lor (b \le a)$ to prove that it is a tautology?

Published on 04 Nov 2013 - 2:00

score 3.8k · Answer 5 · 2026-04-06 23:01:20

3.8k

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Equivalence Relations Proof dealing 3 dividing x + y

Published on 06 Apr 2026 - 23:01

score 129 · Answer 6 · 2026-04-06 23:03:02

129

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Why are both of these not equivalence relations?

Published on 06 Apr 2026 - 23:03

score 74 · Answer 7 · 2026-04-09 01:25:00

74

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homomorphism problem

Published on 09 Apr 2026 - 1:25

score 1.3k · Answer 8 · 2026-03-30 00:22:54

1.3k

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Let R be a relation on set A. Prove that $R^2 \subseteq R <=>$ R is transitive $<=> R^i \subseteq R ,\forall i \geq 1$

Published on 30 Mar 2026 - 0:22

score 82 · Answer 9 · 2013-11-04 23:32:41

82

Views

Proving a relation's inverse's properties by knowing the original's.

Published on 04 Nov 2013 - 23:32

score 109 · Answer 10 · 2013-11-05 03:00:24

109

Views

Proving that the relation $a \le b \iff b - a \ge 0$ is antisymmetric and total.

Published on 05 Nov 2013 - 3:00

score 210 · Answer 11 · 2013-11-05 05:34:35

210

Views

Is this equation to prove that $aRb \iff a^2 - b^2 = 1$ is antisymmetric correct?

Published on 05 Nov 2013 - 5:34

score 197 · Answer 12 · 2013-11-05 13:58:19

197

Views

Anti symmetrical relation

Published on 05 Nov 2013 - 13:58

score 127 · Answer 13 · 2013-11-05 23:07:35

127

Views

Properties of relation $R$ on $\mathbb{N} \times \mathbb{N}:\;(a,b)R(c,d) \iff a -c = b -d$

Published on 05 Nov 2013 - 23:07

score 105 · Answer 14 · 2013-11-06 08:59:37

105

Views

How can I determine that a relation lacks a property without using a counterexample?

Published on 06 Nov 2013 - 8:59

score 84 · Answer 15 · 2013-11-06 11:13:58

84

Views

Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$?

Published on 06 Nov 2013 - 11:13

List Question

How is it possible to have a transitive yet not complete relation?

Proving that $R$ is antisymmetric if and only if $G \cap G^{-1} \subseteq D$

Proving that $aRb \iff a = b \lor a = b^2$ is antisymmetric.

How can I further simplify $(a \le b) \lor (b \le a)$ to prove that it is a tautology?

Equivalence Relations Proof dealing 3 dividing x + y

Why are both of these not equivalence relations?

homomorphism problem

Let R be a relation on set A. Prove that $R^2 \subseteq R <=>$ R is transitive $<=> R^i \subseteq R ,\forall i \geq 1$

Proving a relation's inverse's properties by knowing the original's.

Proving that the relation $a \le b \iff b - a \ge 0$ is antisymmetric and total.

Is this equation to prove that $aRb \iff a^2 - b^2 = 1$ is antisymmetric correct?

Anti symmetrical relation

Properties of relation $R$ on $\mathbb{N} \times \mathbb{N}:\;(a,b)R(c,d) \iff a -c = b -d$

How can I determine that a relation lacks a property without using a counterexample?

Is my transitivity proof correct for the relation over $\mathbb{Z} \times \mathbb{Z}$ where $(a,b)R(c,d) \iff (a \le c \lor b \le d)$?

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