Diclib.com
Словарь ChatGPT

Поиск в словаре Индивидуальные решения

Введите слово или словосочетание на любом языке 👆

Язык:

Перевод и анализ слов искусственным интеллектом ChatGPT

На этой странице Вы можете получить подробный анализ слова или словосочетания, произведенный с помощью лучшей на сегодняшний день технологии искусственного интеллекта:

как употребляется слово
частота употребления
используется оно чаще в устной или письменной речи
варианты перевода слова
примеры употребления (несколько фраз с переводом)
этимология

Что (кто) такое DeMorgan's Theorem - определение

PAIR OF TRANSFORMATION RULES THAT ARE BOTH VALID RULES OF INFERENCE

De Morgan's Laws; DeMorgan's Law; DeMorgan's; De Morgan's law; De Morgan dual; De Morgan laws; De Morgan's theorem; De Morgan duality; De Morgan's Law; Demorgan's law; Demorgan's theorem; DeMorgan's Theory; Demorgans law; DeMorgan's laws; DeMorgan's Laws; De Morgan Laws; De Morgan law; De Morgan theorem; De Morgan’s laws; De Morgan's Theorems; DeMorgan's theorem; De Morgan's Rule; De Morgans laws; DeMorgans Law; De Morgan’s law; De Morgan′s laws; De morgan's theorem; Demorgan's Laws; Demorgan Law; De Morgan's theorems; DeMorgan's law; Negation of conjunction; Negation of disjunction; DeMorgan's Theorems; De Morgan's laws for quantifiers; De Morgan duality expressions; De Morgan rules

Найдено результатов: 1938

DeMorgan's theorem

<logic> A logical theorem which states that the complement of a conjunction is the disjunction of the complements or vice versa. In symbols: not (x and y) = (not x) or (not y) not (x or y) = (not x) and (not y) E.g. if it is not the case that I am tall and thin then I am either short or fat (or both). The theorem can be extended to combinations of more than two terms in the obvious way. The same laws also apply to sets, replacing logical complement with set complement, conjunction ("and") with set intersection, and disjunction ("or") with set union. A (C) programmer might use this to re-write if (!foo && !bar) ... as if (!(foo || bar)) ... thus saving one operator application (though an {optimising compiler} should do the same, leaving the programmer free to use whichever form seemed clearest). (1995-12-14)

De Morgan's laws

In propositional logic and Boolean algebra, De Morgan's lawsCopi and CohenMoore and Parker are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician.

https://en.wikipedia.org/wiki/De_Morgan's_laws

Divergence theorem

$</math> approaches <math>\operatorname{div} \mathbf{F}</math>$

GENERALIZATION OF THE FUNDAMENTAL THEOREM IN VECTOR CALCULUS

Gauss' theorem; Gauss's theorem; Gauss theorem; Ostrogradsky-Gauss theorem; Ostrogradsky's theorem; Gauss's Theorem; Divergence Theorem; Gauss' divergence theorem; Ostrogradsky theorem; Gauss-Ostrogradsky theorem; Gauss Ostrogradsky theorem; Gauss–Ostrogradsky theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

https://en.wikipedia.org/wiki/Divergence_theorem

theorem

IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED

Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem

n.

Proposition (to be demonstrated), position, dictum, thesis.

Well-ordering theorem

SET-THEORETIC THEOREM OR PRINCIPLE, EQUIVALENT TO THE AXIOM OF CHOICE

Well ordering theorem; Zermelo's well-ordering theorem; Wellordering theorem; Zermelo's theorem; Zermelo Theorem

In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering.

https://en.wikipedia.org/wiki/Well-ordering_theorem

Wedderburn's little theorem

THEOREM

Wedderburn theorem; Wedderburn Theorem

In mathematics, Wedderburn's little theorem states that every finite domain is a field. In other words, for finite rings, there is no distinction between domains, division rings and fields.

https://en.wikipedia.org/wiki/Wedderburn's_little_theorem

Theorem

IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED

Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem

·vt To formulate into a theorem.

II. Theorem ·noun A statement of a principle to be demonstrated.

III. Theorem ·noun That which is considered and established as a principle; hence, sometimes, a rule.

Pappus's centroid theorem

THEOREM THAT, FOR A SOLID OF REVOLUTION OF A PLANAR FIGURE, THE SURFACE AREA EQUALS THE FIGURE’S PERIMETER TIMES THE DISTANCE THE PERIMETER’S CENTROID TRAVELS, AND THE VOLUME EQUALS THE FIGURE’S AREA TIMES THE DISTANCE THE FIGURE’S CENTROID TRAVEL

Pappus-Guldinus theorem; Guldinus theorem; Theorem of Pappus; First theorem of pappus; Pappus centroid theorem; Pappus–Guldinus theorem; Theorem of papus; Theorem of Papus

In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution.

https://en.wikipedia.org/wiki/Pappus's_centroid_theorem

theorem

IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED

Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem

n.

1) to deduce, formulate a theorem

2) to prove; test a theorem

3) a binomial theorem

theorem

IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED

Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem

(theorems)

A theorem is a statement in mathematics or logic that can be proved to be true by reasoning.

N-COUNT

Википедия

De Morgan's laws

In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation.

The rules can be expressed in English as:

The negation of a disjunction is the conjunction of the negations
The negation of a conjunction is the disjunction of the negations

or

The complement of the union of two sets is the same as the intersection of their complements
The complement of the intersection of two sets is the same as the union of their complements

or

not (A or B) = (not A) and (not B)
not (A and B) = (not A) or (not B)

where "A or B" is an "inclusive or" meaning at least one of A or B rather than an "exclusive or" that means exactly one of A or B.

In set theory and Boolean algebra, these are written formally as

{\begin{aligned}{\overline {A\cup B}}&={\overline {A}}\cap {\overline {B}},\\{\overline {A\cap B}}&={\overline {A}}\cup {\overline {B}},\end{aligned}}

where

$A$ and $B$ are sets,
${\overline {A}}$ is the complement of $A$ ,
$\cap$ is the intersection, and
$\cup$ is the union.

In formal language, the rules are written as

\neg (P\lor Q)\iff (\neg P)\land (\neg Q),

and

\neg (P\land Q)\iff (\neg P)\lor (\neg Q)

where

P and Q are propositions,
$\neg$ is the negation logic operator (NOT),
$\land$ is the conjunction logic operator (AND),
$\lor$ is the disjunction logic operator (OR),
$\iff$ is a metalogical symbol meaning "can be replaced in a logical proof with", often read as "if and only if". For any combination of true/false values for P and Q, the left and right sides of the arrow will hold the same truth value after evaluation.

Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality.

https://en.wikipedia.org/wiki/De Morgan's laws