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# 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). 

90 relations: Abelian group, Adder (electronics), Addition, Affirming a disjunct, Algebraic normal form, Alpha compositing, Analytic philosophy, Antecedent (logic), Arity, Associative property, Barber paradox, Binary number, Bitwise operation, Boolean algebra, Boolean domain, Boolean function, Boolean-valued function, Bounding volume, C (programming language), C Sharp (programming language), C++, Caret, Carry (arithmetic), Commutative property, Computer graphics, Controlled NOT gate, Cryptography, Cursor (user interface), D (programming language), De Morgan's laws, Direct sum of modules, Disjunctive syllogism, Distributive property, Doubly linked list, English language, Feistel cipher, Field (mathematics), First-order logic, GF(2), Group (mathematics), Hadamard transform, Hardware random number generator, Idempotence, If and only if, Independence (probability theory), Infix, Involution (mathematics), Isomorphism, Java (programming language), Linguistics, ... Expand index (40 more) »

## Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

## Adder (electronics)

An adder is a digital circuit that performs addition of numbers.

## Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

## 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.

## Algebraic normal form

In Boolean algebra, the algebraic normal form (ANF), ring sum normal form (RSNF or RNF), Zhegalkin normal form, or Reed–Muller expansion is a way of writing logical formulas in one of three subforms.

## Alpha compositing

In computer graphics, alpha compositing is the process of combining an image with a background to create the appearance of partial or full transparency.

## Analytic philosophy

Analytic philosophy (sometimes analytical philosophy) is a style of philosophy that became dominant in the Western world at the beginning of the 20th century.

## Antecedent (logic)

An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause.

## 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.

## Barber paradox

The barber paradox is a puzzle derived from Russell's paradox.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## 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.

## Bounding volume

In computer graphics and computational geometry, a bounding volume for a set of objects is a closed volume that completely contains the union of the objects in the set.

## C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

## C Sharp (programming language)

C# (/si: ʃɑːrp/) is a multi-paradigm programming language encompassing strong typing, imperative, declarative, functional, generic, object-oriented (class-based), and component-oriented programming disciplines.

## C++

C++ ("see plus plus") is a general-purpose programming language.

## Caret

The caret is an inverted V-shaped grapheme.

## Carry (arithmetic)

In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits.

## Commutative property

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

## Computer graphics

Computer graphics are pictures and films created using computers.

## Controlled NOT gate

In computing science, the controlled NOT gate (also C-NOT or CNOT) is a quantum gate that is an essential component in the construction of a quantum computer.

## Cryptography

Cryptography or cryptology (from κρυπτός|translit.

## Cursor (user interface)

In computer user interfaces, a cursor is an indicator used to show the current position for user interaction on a computer monitor or other display device that will respond to input from a text input or pointing device.

## D (programming language)

D is an object-oriented, imperative, multi-paradigm system programming language created by Walter Bright of Digital Mars and released in 2001.

## 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.

## Direct sum of modules

In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module.

## 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.

## Doubly linked list

In computer science, a doubly linked list is a linked data structure that consists of a set of sequentially linked records called nodes.

## English language

English is a West Germanic language that was first spoken in early medieval England and is now a global lingua franca.

## Feistel cipher

In cryptography, a Feistel cipher is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel who did pioneering research while working for IBM (USA); it is also commonly known as a Feistel network.

## Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

## 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.

## GF(2)

GF(2) (also F2, Z/2Z or Z2) is the '''G'''alois '''f'''ield of two elements.

## Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

## Hadamard transform

The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms.

## Hardware random number generator

In computing, a hardware random number generator (true random number generator, TRNG) is a device that generates random numbers from a physical process, rather than a computer program.

## 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.

## 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.

## Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

## Infix

An infix is an affix inserted inside a word stem (an existing word).

## Involution (mathematics)

In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.

## Isomorphism

In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.

## Java (programming language)

Java is a general-purpose computer-programming language that is concurrent, class-based, object-oriented, and specifically designed to have as few implementation dependencies as possible.

## Linguistics

Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context.

## List of Boolean algebra topics

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

## List of logic symbols

In logic, a set of symbols is commonly used to express logical representation.

## Logical biconditional

In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "P if and only if Q", where P is an antecedent and Q is a consequent.

## 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 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.

## 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.

## Logical NOR

In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or.

## Material conditional

The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".

## MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

## Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

## Monoid

In abstract algebra, a branch of mathematics, a monoid is an algebraic structure with a single associative binary operation and an identity element.

## Monotonic function

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

## 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.

## Neural network

The term neural network was traditionally used to refer to a network or circuit of neurons.

## One-time pad

In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a one-time pre-shared key the same size as, or longer than, the message being sent.

## Operand

In mathematics an operand is the object of a mathematical operation, i.e. it is the quantity that is operated on.

## Operation (mathematics)

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

## Paradoxes of material implication

The paradoxes of material implication are a group of formulae that are truths of classical logic but are intuitively problematic.

## Parity (mathematics)

In mathematics, parity is the property of an integer's inclusion in one of two categories: even or odd.

## Parity bit

A parity bit, or check bit, is a bit added to a string of binary code to ensure that the total number of 1-bits in the string is even or odd.

## Perl

Perl is a family of two high-level, general-purpose, interpreted, dynamic programming languages, Perl 5 and Perl 6.

## PHP

PHP: Hypertext Preprocessor (or simply PHP) is a server-side scripting language designed for Web development, but also used as a general-purpose programming language.

## 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.

## Propositional calculus

Propositional calculus is a branch of logic.

## Python (programming language)

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

## RAID

RAID (Redundant Array of Independent Disks, originally Redundant Array of Inexpensive Disks) is a data storage virtualization technology that combines multiple physical disk drive components into one or more logical units for the purposes of data redundancy, performance improvement, or both.

## Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

## Ruby (programming language)

Ruby is a dynamic, interpreted, reflective, object-oriented, general-purpose programming language.

## Rule 90

In the mathematical study of cellular automata, Rule 90 is an elementary cellular automaton based on the exclusive or function.

## Symmetric difference

In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection.

## 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.

## Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

## Venn diagram

A Venn diagram (also called primary diagram, set diagram or logic diagram) is a diagram that shows all possible logical relations between a finite collection of different sets.

## Wolfram Research

Wolfram Research is a private company that creates computational technology.

## XOR cipher

In cryptography, the simple XOR cipher is a type of additive cipher, an encryption algorithm that operates according to the principles: where \oplus denotes the exclusive disjunction (XOR) operation.

## XOR gate

The XOR gate (sometimes EOR gate, or EXOR gate and pronounced as Exclusive OR gate) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd.

## XOR linked list

An XOR linked list is a data structure used in computer programming.

## XOR swap algorithm

In computer programming, the XOR swap is an algorithm that uses the XOR bitwise operation to swap values of distinct variables having the same data type without using a temporary variable.

## References

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