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# Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true. [1]

61 relations: Affirming a disjunct, Arity, Associative property, Bit field, Bitwise operation, Boolean algebra, Boolean domain, Boolean function, Boolean-valued function, Commutative property, Complement (set theory), Constructivism (mathematics), Control flow, Curry–Howard correspondence, De Morgan's laws, Disjunction elimination, Disjunction introduction, Disjunctive syllogism, Distributive property, Element (mathematics), Exclusive or, Existential quantification, First-order logic, Fréchet inequalities, George Boole, Idempotence, Identity element, If and only if, Intersection (set theory), Jan Łukasiewicz, JavaScript, Józef Maria Bocheński, List of Boolean algebra topics, Literal (mathematical logic), Logic, Logical conjunction, Logical connective, Logical graph, Mathematical logic, Mathematics, Meaning (linguistics), Monotonic function, Natural language, Negation, Operation (mathematics), Operator (computer programming), OR gate, Programming language, Proposition, Propositional calculus, ... Expand index (11 more) »

## Affirming a disjunct

The formal fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct or a false exclusionary disjunct occurs when a deductive argument takes the following logical form: Or in logical operators: Where \vdash denotes a logical assertion.

## Arity

In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.

## Associative property

In mathematics, the associative property is a property of some binary operations.

## Bit field

A bit field is a data structure used in computer programming.

## Bitwise operation

In digital computer programming, a bitwise operation operates on one or more bit patterns or binary numerals at the level of their individual bits.

## Boolean algebra

In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.

## Boolean domain

In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true.

## Boolean function

In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ: Bk → B, where B.

## Boolean-valued function

A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f: X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B.

## Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

## Complement (set theory)

In set theory, the complement of a set refers to elements not in.

## Constructivism (mathematics)

In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.

## Control flow

In computer science, control flow (or flow of control) is the order in which individual statements, instructions or function calls of an imperative program are executed or evaluated.

## Curry–Howard correspondence

In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.

## De Morgan's laws

In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.

## Disjunction elimination

In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or or elimination), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.

## Disjunction introduction

Disjunction introduction or addition (also called or introduction) is a rule of inference of propositional logic and almost every other deduction system.

## Disjunctive syllogism

In classical logic, disjunctive syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.

## Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

## Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

## Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

## Existential quantification

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".

## First-order logic

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

## Fréchet inequalities

In probabilistic logic, the Fréchet inequalities, also known as the Boole–Fréchet inequalities, are rules implicit in the work of George BooleBoole, G. (1854).

## George Boole

George Boole (2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland.

## Idempotence

Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.

## Identity element

In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

## Jan Łukasiewicz

Jan Łukasiewicz (21 December 1878 – 13 February 1956) was a Polish logician and philosopher born in Lwów, a city in the Galician kingdom of Austria-Hungary.

## JavaScript

JavaScript, often abbreviated as JS, is a high-level, interpreted programming language.

## Józef Maria Bocheński

Józef Maria Bocheński (Czuszów, Congress Poland, Russian Empire, 30 August 1902 – 8 February 1995, Fribourg, Switzerland) was a Polish Dominican, logician and philosopher.

## List of Boolean algebra topics

This is a list of topics around Boolean algebra and propositional logic.

## Literal (mathematical logic)

In mathematical logic, a literal is an atomic formula (atom) or its negation.

## Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

## Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

## Logical connective

In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.

## Logical graph

A logical graph is a special type of diagramatic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic.

## Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Meaning (linguistics)

In linguistics, meaning is the information or concepts that a sender intends to convey, or does convey, in communication with a receiver.

## Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

## Natural language

In neuropsychology, linguistics, and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation.

## Negation

In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.

## Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

## Operator (computer programming)

Programming languages typically support a set of operators: constructs which behave generally like functions, but which differ syntactically or semantically from usual functions.

## OR gate

The OR gate is a digital logic gate that implements logical disjunctionit behaves according to the truth table to the right.

## Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

## Proposition

The term proposition has a broad use in contemporary analytic philosophy.

## Propositional calculus

Propositional calculus is a branch of logic.

## Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

## Sequence point

A sequence point defines any point in a computer program's execution at which it is guaranteed that all side effects of previous evaluations will have been performed, and no side effects from subsequent evaluations have yet been performed.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Short-circuit evaluation

Short-circuit evaluation, minimal evaluation, or McCarthy evaluation (after John McCarthy) is the semantics of some Boolean operators in some programming languages in which the second argument is executed or evaluated only if the first argument does not suffice to determine the value of the expression: when the first argument of the AND function evaluates to false, the overall value must be false; and when the first argument of the OR function evaluates to true, the overall value must be true.

## Tagged union

In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, or sum type, is a data structure used to hold a value that could take on several different, but fixed, types.

## Truth function

In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values.

## Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).

## Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

## Union (set theory)

In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

## Vacuous truth

In mathematics and logic, a vacuous truth is a statement that asserts that all members of the empty set have a certain property.

## William Stanley Jevons

William Stanley Jevons FRS (1 September 1835 – 13 August 1882) was an English economist and logician.

## References

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