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disjunct

▪ I. † disˈjunct, n. Sc. Latinized form of disjoint n.1513 [see disjoint n.].▪ II. disjunct, a. and n. (dɪsˈdʒʌŋkt) [ad. L. disjunct-us, pa. pple. of disjungĕre to disjoin. Cf. disjoint a.] A. adj. 1. a. Disjoined, disconnected, separated, separate, distinct; † distant. (Now rare exc. in technical s... Oxford English Dictionary

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Disjunct

The term disjunct can refer to: disjunct (linguistics) disjunct or quincunx in astrology, an aspect made when two planets are 150 degrees, or five signs apart a disjunct distribution in biology, one in which two closely related taxa are widely separated geographically disjunct (music), a melodic skip wikipedia.org

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Disjunct (linguistics)

In linguistics, a disjunct is a type of adverbial adjunct that expresses information that is not considered essential to the sentence it appears in, but Hopefully "Hopefully" is an example of a word whose use as a disjunct ("it is hoped") is sometimes controversial. wikipedia.org

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disjunct set D is tautological $\iff$ D contains both p and $\neg p$ We say that a set of literals D has model the interpretation I, if which there's a literal p in D, s.t. $I \models p$. D is tautological if every in...

For every interpretation $I$ exactly one of $p$ and $¬p$ is evaluated to TRUE. Thus, for every $I$ we have that $I \vDash D$, and this means that $D$ is tautological. For the vice versa, assume that $D$ is tautological and that there is no atom negated and unnegated. If so, we can define an interpre...

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Disjunct matrix

The following relationships are "well-known": Every -separable matrix is also -disjunct. Every -disjunct matrix is also -separable. The following matrix is -separable (and thus 2-disjunct) but not 3-disjunct. wikipedia.org

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Meanings of the terms "conjunct" and "disjunct" in a logic? This sentential logic problem is stated as: Suppose that $A \models B$, where $A$ is a conjunction of literals and $B$ is a disjunction of literals. Show tha...

If $A = p \land q$ (so $A$ is a conjunction of literals), and $B = r\lor s$ (so $B$ is a disjunct of literals), then $p, q$ are each conjuncts of $A$ If $B = Q_1 \lor Q_2 \lor \cdots \lor Q_m,\;$ then any literal $\,Q_j$ is a disjunct of $B\;$ (where $1\leq j\leq m$).

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Disjunct distribution

In biology, a taxon with a disjunct distribution is one that has two or more groups that are related but considerably separated from each other geographically Range fragmentation Also called range fragmentation, disjunct distributions may be caused by changes in the environment, such as mountain building and wikipedia.org

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Are 2 dependent probabilities always disjunct? If $2$ probabilities are disjunct then they are not independent. Are any $2$ dependent probabilities also disjunct? Modus ponens for instance are $2$ dependent and mutual...

I am assuming that disjunct probabilities mean that the events are mutually exclusive (disjoint as sets). Dependent probabilities need not be 'disjunct'. For example, roll a die twice.

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Can a mathematical difference not also imply a disjunction? Is there a disjunction for every difference? E.g. 2-1=1 which implies a disjunction e.g. the sets 1 and 2 are disjunct. So can there not be any difference th...

The claim that numbers are sets is controversial; if they are not sets, talk of them being ‘disjoint’ doesn't make sense. If one does identify numbers with sets, the best-known way of doing so is von Neumann's, on which each number is the set of its predecessors, so that in particular $0=∅$, $1=\\{∅...

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prove that $A_n$ is the disjunct union of $B_1$ and $B_2$ prove that $A_n$ is the disjunct union of $B_1$ and $B_2$ Suppose we have $B_1 = \left(\cup_{i=1}^{n} A_i\right) \backslash \left(\cup_{i=1}^{n-1} A_i\right)$...

Note that $$B_2 = \bigcup_{i=1}^{n-1} (A_i \cap A_n) = \left(\bigcup_{i=1}^{n-1} A_i \right) \cap A_n$$ and $$\begin{align*} B_1 &= \left( \bigcup_{i=1}^n A_i \right) \backslash \left( \bigcup_{i=1}^{n-1} A_i \right) \\\ &= \left( \bigcup_{i=1}^{n-1} A_i \cup A_n \right) \backslash \left( \bigcup_{i...

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How to disjunct $\forall x.(P(x) \lor Q(x)) $ I really don't understand how to disjunct this. The whole argument is: $$\forall x.[P(x) \lor Q(x)] \rightarrow \neg[\exists x.P(x)] \rightarrow \forall x. Q(x) $$ Am I...

Before give a hint, I rewrite your attempt. As I see, you try to prove $$ \vdash ∀x.[P(x)∨Q(x)]→[¬∃x.P(x)→∀x.Q(x)]. $$ You try to use deduction **theorem** so you try to prove $$ ∀x.[P(x)∨Q(x)]\,;\,\lnot [\exists P(x)]\vdash \forall x.Q(x) $$ by De Morgan's theorem you get $\vdash\lnot\exists x.P(x)...

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Split $\mathbb{N}$ into a countable union of countable sets. A friend thought of this problem and I found it interesting to think about so I want to share it with you. I am intrigued how you will solve the problem. F...

Let $U_i=\\{2^in\colon n\text{ is an odd natural number}\\}$.

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Covering the natural numbers with countable amount of disjunct sequences? I have got the following question: Can you cover $\mathbb{N}$ with countable amount of arithmetic, disjunct sequences(their difference can...

**Hint** There is a well known solution: $$\\{2n, 4n+1,8n-1,\cdots \\}$$ which are of the form $2^kn+u_k$ with $u_k$ is the residue closest to $0$ which has not been previously covered All integers are of the form $2n$ or $2n+1$ so we choose the **first sequence** $2n$ we cover all even numbers. We ...

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Completion of incomplete claim about General Set Theory (GST) in Wiki article In the Wikipedia article on General Set Theory (GST), there is a claim in the section on metamathematics that seems to be missing a disjunc...

The "either" is likely a typo. An axiom schema is a rule for constructing an infinite number of axioms, all of which must have a given form. Not "finitely axiomatizable" means exactly what it sounds like. The set of consequences of the theory are not provable from a finite set of axioms. So here wha...

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Distance between sets in $\mathbb{R}^p$ Let $A$ and $B$ be closed, bounded, disjunct subsets of $\mathbb{R}^p$ Now, this is not a metric, but define $\delta$ like this: $$ \delta = \inf V, $$ where $$ V = \\{ \| a-b ...

Briefly to say, if $\inf V=0$, then there are sequences $\\{a_i\\}, \\{b_i\\}$ such that $\Vert a_i-b_i\Vert$ tend to zero. But, then, by the boundedness of $A,B$, we can find convergent subsequences of $\\{a_{k_i}\\}, \\{b_{k_i}\\}$ respectively, and these two subsequences will have the same limit,...

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disjunct

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disjunct

Disjunct

Disjunct (linguistics)

disjunct set D is tautological $\iff$ D contains both p and $\neg p$ We say that a set of literals D has model the interpretation I, if which there's a literal p in D, s.t. $I \models p$. D is tautological if every in...

Disjunct matrix

Meanings of the terms "conjunct" and "disjunct" in a logic? This sentential logic problem is stated as: Suppose that $A \models B$, where $A$ is a conjunction of literals and $B$ is a disjunction of literals. Show tha...

Disjunct distribution

Are 2 dependent probabilities always disjunct? If $2$ probabilities are disjunct then they are not independent. Are any $2$ dependent probabilities also disjunct? Modus ponens for instance are $2$ dependent and mutual...

Can a mathematical difference not also imply a disjunction? Is there a disjunction for every difference? E.g. 2-1=1 which implies a disjunction e.g. the sets 1 and 2 are disjunct. So can there not be any difference th...

prove that $A_n$ is the disjunct union of $B_1$ and $B_2$ prove that $A_n$ is the disjunct union of $B_1$ and $B_2$ Suppose we have $B_1 = \left(\cup_{i=1}^{n} A_i\right) \backslash \left(\cup_{i=1}^{n-1} A_i\right)$...

How to disjunct $\forall x.(P(x) \lor Q(x)) $ I really don't understand how to disjunct this. The whole argument is: $$\forall x.[P(x) \lor Q(x)] \rightarrow \neg[\exists x.P(x)] \rightarrow \forall x. Q(x) $$ Am I...

Split $\mathbb{N}$ into a countable union of countable sets. A friend thought of this problem and I found it interesting to think about so I want to share it with you. I am intrigued how you will solve the problem. F...

Covering the natural numbers with countable amount of disjunct sequences? I have got the following question: Can you cover $\mathbb{N}$ with countable amount of arithmetic, disjunct sequences(their difference can...

Completion of incomplete claim about General Set Theory (GST) in Wiki article In the Wikipedia article on General Set Theory (GST), there is a claim in the section on metamathematics that seems to be missing a disjunc...

Distance between sets in $\mathbb{R}^p$ Let $A$ and $B$ be closed, bounded, disjunct subsets of $\mathbb{R}^p$ Now, this is not a metric, but define $\delta$ like this: $$ \delta = \inf V, $$ where $$ V = \\{ \| a-b ...