Question

Without the Axiom of Choice, must two nonempty sets have a surjection between them?

score 144 · Answer 1 · 2018-10-09 15:50:58

144

Views

Without the Axiom of Choice, must two nonempty sets have a surjection between them?

Published on 09 Oct 2018 - 15:50

score 1.6k · Answer 2 · 2026-03-22 02:06:30

1.6k

Views

For$ a, b \in \mathbb{Z}$ define $a\sim b$, if and only if $a^2 – b^2$ is divisible by $3$.

Published on 22 Mar 2026 - 2:06

score 23 · Answer 3 · 2018-10-10 09:57:45

23

Views

Proving unit relation features

Published on 10 Oct 2018 - 9:57

score 30 · Answer 4 · 2018-10-13 04:41:28

30

Views

If $R_{1}$, $R_{2}$, and $R = R_{1} \cap R_{2}$ are relations on $A$, with reflexive closures $S_{1}$, $S_{2}$, and $S$, then $S_{1} \cap S_{2} = S$?

Published on 13 Oct 2018 - 4:41

score 270 · Answer 5 · 2018-10-14 22:52:27

270

Views

$S = \{(x,y): x \text{ is a sibling of } y\}$. Why is this relation not transitive?

Published on 14 Oct 2018 - 22:52

score 61 · Answer 6 · 2026-03-25 12:48:40

61

Views

Is the following relation considered symmetric?

Published on 25 Mar 2026 - 12:48

score 539 · Answer 7 · 2018-10-17 14:41:20

539

Views

What are relations?

Published on 17 Oct 2018 - 14:41

score 391 · Answer 8 · 2018-10-18 21:08:19

391

Views

Empty relation on non-empty set - is it reflexive?

Published on 18 Oct 2018 - 21:08

score 1.2k · Answer 9 · 2026-03-25 09:32:06

1.2k

Views

Prove/disprove, that the relation is reflexive, symmetric, antisymmetric and transitive

Published on 25 Mar 2026 - 9:32

score 84 · Answer 10 · 2018-10-19 22:01:17

84

Views

Minimal Element Definition Independent of Partial Order?

Published on 19 Oct 2018 - 22:01

score 345 · Answer 11 · 2018-10-20 21:43:26

345

Views

Find the symmetric subsets of $B = \{1,2,3,4\}$

Published on 20 Oct 2018 - 21:43

score 105 · Answer 12 · 2018-10-21 13:24:41

105

Views

Transitive closure applied to a relation

Published on 21 Oct 2018 - 13:24

score 36 · Answer 13 · 2018-10-22 12:18:13

36

Views

antisymmetric proof clarification

Published on 22 Oct 2018 - 12:18

score 393 · Answer 14 · 2026-03-22 14:29:23

393

Views

Question about the defining equivalence relations on sets

Published on 22 Mar 2026 - 14:29

score 210 · Answer 15 · 2018-10-24 14:23:01

210

Views

If $xR_1y$ if $x^2 + y^2$ is divisible by $5$, is the relation transitive?

Published on 24 Oct 2018 - 14:23

List Question

Without the Axiom of Choice, must two nonempty sets have a surjection between them?

For$ a, b \in \mathbb{Z}$ define $a\sim b$, if and only if $a^2 – b^2$ is divisible by $3$.

Proving unit relation features

If $R_{1}$, $R_{2}$, and $R = R_{1} \cap R_{2}$ are relations on $A$, with reflexive closures $S_{1}$, $S_{2}$, and $S$, then $S_{1} \cap S_{2} = S$?

$S = \{(x,y): x \text{ is a sibling of } y\}$. Why is this relation not transitive?

Is the following relation considered symmetric?

What are relations?

Empty relation on non-empty set - is it reflexive?

Prove/disprove, that the relation is reflexive, symmetric, antisymmetric and transitive

Minimal Element Definition Independent of Partial Order?

Find the symmetric subsets of $B = \{1,2,3,4\}$

Transitive closure applied to a relation

antisymmetric proof clarification

Question about the defining equivalence relations on sets

If $xR_1y$ if $x^2 + y^2$ is divisible by $5$, is the relation transitive?

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