Question

Attempt to prove the $∀d∀x∀y (d | x ∧ d | y ∧ x ≤ y → d | y- x)$ property of the “divides” relation for non-negative integers

score 58 · Answer 1 · 2026-03-27 06:09:16

58

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Attempt to prove the $∀d∀x∀y (d | x ∧ d | y ∧ x ≤ y → d | y- x)$ property of the “divides” relation for non-negative integers

Published on 27 Mar 2026 - 6:09

score 120 · Answer 2 · 2026-03-27 06:07:22

120

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Proving $∀x (x ≠ 0 → gcd(x, 0) = x)$ formally attempt

Published on 27 Mar 2026 - 6:07

score 49 · Answer 3 · 2017-04-05 05:26:23

49

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How to prove that this argument is valid?

Published on 05 Apr 2017 - 5:26

score 62 · Answer 4 · 2017-04-05 10:08:51

Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.

score 156 · Answer 5 · 2017-04-05 10:42:33

$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$

score 251 · Answer 6 · 2026-03-25 20:34:33

251

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Translate into notation of predicate logic with Domain

Published on 25 Mar 2026 - 20:34

score 19 · Answer 7 · 2026-03-29 22:07:39

19

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(Predicate Logic) ∀x ∈ N(x > 1 → ∃k ∈ N∃m ∈ N(m ≡ 1(mod 2) ∧ x = 2^k⋅m))

Published on 29 Mar 2026 - 22:07

score 193 · Answer 8 · 2017-04-07 18:01:49

193

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Predicate Logic - Prove or disprove

Published on 07 Apr 2017 - 18:01

score 156 · Answer 9 · 2026-03-29 19:10:01

156

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Is this quantifier statement $(\forall x)(\phi (x) \implies \psi(x)) \implies ((\forall x)\phi(x)\implies (\forall x)\psi (x)) $ always true?

Published on 29 Mar 2026 - 19:10

score 233 · Answer 10 · 2023-02-02 08:16:21

233

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Contrapositive, Converse and Inverse of statements with multiple quantifiers

Published on 02 Feb 2023 - 8:16

score 173 · Answer 11 · 2026-03-25 23:34:56

173

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Mixing predicate logic with propositional logic

Published on 25 Mar 2026 - 23:34

score 71 · Answer 12 · 2026-03-26 01:02:45

71

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Have I misunderstood this argument about truth values?

Published on 26 Mar 2026 - 1:02

score 252 · Answer 13 · 2023-02-11 05:59:18

252

Views

What's the converse proposition of $\forall x(P(x)\implies Q(x))$?

Published on 11 Feb 2023 - 5:59

score 141 · Answer 14 · 2023-02-11 12:33:06

141

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Notation to assign a statement or predicate to a symbol

Published on 11 Feb 2023 - 12:33

score 51 · Answer 15 · 2023-02-14 09:29:14

51

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Predicate theory having a model, what are the consequences?

Published on 14 Feb 2023 - 9:29

List Question

Attempt to prove the $∀d∀x∀y (d | x ∧ d | y ∧ x ≤ y → d | y- x)$ property of the “divides” relation for non-negative integers

Proving $∀x (x ≠ 0 → gcd(x, 0) = x)$ formally attempt

How to prove that this argument is valid?

Prove the statement $\forall x\in\mathbb N (x > 1\to\exists k\in\mathbb N\exists m \in\mathbb N (m \equiv 1 (\text{mod }2) \wedge x = 2^km))$.

$\forall x\in\mathbb{N}[(\exists y\in\mathbb{N}(2\leq y\land y<x\land y\ |\ x))\to(\exists z\in\mathbb{N}(2\leq z\land z\leq\sqrt x\land z\ |\ x))]$

Translate into notation of predicate logic with Domain

(Predicate Logic) ∀x ∈ N(x > 1 → ∃k ∈ N∃m ∈ N(m ≡ 1(mod 2) ∧ x = 2^k⋅m))

Predicate Logic - Prove or disprove

Is this quantifier statement $(\forall x)(\phi (x) \implies \psi(x)) \implies ((\forall x)\phi(x)\implies (\forall x)\psi (x)) $ always true?

Contrapositive, Converse and Inverse of statements with multiple quantifiers

Mixing predicate logic with propositional logic

Have I misunderstood this argument about truth values?

What's the converse proposition of $\forall x(P(x)\implies Q(x))$?

Notation to assign a statement or predicate to a symbol

Predicate theory having a model, what are the consequences?

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