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Exclusive or: Alternative symbols, Computer science & Properties

Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd.

Language: English [EN]
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Exclusive or topic overview

The analysis highlights Alternative symbols, Computer science and Properties as prominent areas in the source structure around Exclusive or.

Related topics
94
Source areas
9
Connected nodes
103
Extracted relationships
56
Concept neighborhoods
23
Bridge connections
103

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Alternative symbols · 25 topics
Computer science · 21 topics
Properties · 12 topics
Relation to modern algebra · 10 topics
Exclusive or in natural language · 9 topics
Overview · 8 topics
Equivalences, elimination, and introduction · 6 topics
Encodings · 2 topics
Definition · 1 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

0-preserving
yes
1-preserving
no
Affine
yes
Conjunctive
( x ¯ + y ¯ ) ⋅ ( x + y ) {\displaystyle ({\overline {x}}+{\overline {y}})\cdot (x+y)}
Disjunctive
x ¯ ⋅ y + x ⋅ y ¯ {\displaystyle {\overline {x}}\cdot y+x\cdot {\overline {y}}}
Monotone
no

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Definition

Equivalences, elimination, and introduction

Relation to modern algebra

Exclusive or in natural language

Alternative symbols

Properties

Computer science

Encodings

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Exclusive or connects Entity context

The extracted context around Exclusive or shows recurring relationship patterns in the source. For example, Exclusive or → Algebra, Alonzo Church, Although, Although Boole, Bocheński, Bocheński's, Boole, Charles Sanders Peirce, Christine Ladd-Franklin, Claude Shannon, Edward Vermilye Huntington, Ernst Schröder, Furthermore, George Boole, Giuseppe Peano, Gottfried Wilhelm Leibniz, Hugh MacColl, Huntington, In, Izrail Solomonovich Gradshtein Another extracted example is Exclusive or → yes. Use these groups to spot repeated connection types before inspecting the individual relationships.

Exclusive or

Top relations

related to Alternative symbols · 43
Exclusive or → Algebra, Alonzo Church, Although, Although Boole, Bocheński, Bocheński's, Boole, Charles Sanders Peirce, Christine Ladd-Franklin, Claude Shannon, Edward Vermilye Huntington, Ernst Schröder, Furthermore, George Boole, Giuseppe Peano, Gottfried Wilhelm Leibniz, Hugh MacColl, Huntington, In, Izrail Solomonovich Gradshtein
0-preserving · 1
Exclusive or → yes
1-preserving · 1
Exclusive or → no
Affine · 1
Exclusive or → yes
Conjunctive · 1
Exclusive or → ( x ¯ + y ¯ ) ⋅ ( x + y ) {\displaystyle ({\overline {x}}+{\overline {y}})\cdot (x+y)}
Disjunctive · 1
Exclusive or → x ¯ ⋅ y + x ⋅ y ¯ {\displaystyle {\overline {x}}\cdot y+x\cdot {\overline {y}}}
Monotone · 1
Exclusive or → no
Self-dual · 1
Exclusive or → no
Truth table · 1
Exclusive or → ( 0110 ) {\displaystyle (0110)}
Zhegalkin polynomial · 1
Exclusive or → x ⊕ y {\displaystyle x\oplus y}

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle disjunction exclusive xor used also one true two negation operator logical nleftrightarrow oplus vee operation operators example number logic

Exclusive or relationships Subject–Predicate–Object triples

TTTA extracted 56 structured relationships around Exclusive or. Examples in this analysis include Exclusive or → 0-preserving → yes and Exclusive or → 1-preserving → no. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Exclusive or0-preservingyes1.00infobox
Exclusive or1-preservingno1.00infobox
Exclusive orAffineyes1.00infobox
Exclusive orConjunctive( x ¯ + y ¯ ) ⋅ ( x + y ) {\displaystyle ({\overline {x}}+{\overline {y}})\cdot (x+y)}1.00infobox
Exclusive orDisjunctivex ¯ ⋅ y + x ⋅ y ¯ {\displaystyle {\overline {x}}\cdot y+x\cdot {\overline {y}}}1.00infobox
Exclusive orMonotoneno1.00infobox
Exclusive orSelf-dualno1.00infobox
Exclusive orTruth table( 0110 ) {\displaystyle (0110)}1.00infobox
Exclusive orZhegalkin polynomialx ⊕ y {\displaystyle x\oplus y}1.00infobox
the above have motivated analyses of the exclusivity inference as pragmatic conversational implicatures calculated on the basis of an inclusive semanticsinstance ofNobody ate either rice or beans.Examples0.80text
French soit... soitinstance ofmany languages have disjunctive constructions which are robustly exclusive0.80text
AESinstance ofXOR is also heavily used in block ciphers0.80text

Related concept clusters Concept neighborhoods

The concept neighborhoods around Exclusive or bring nearby vocabulary together. In this analysis, examples include Displaystyle, Negation and Bitwise. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Exclusive or
    • Displaystyle
    • Negation
    • Bitwise
    • May
    • Vee
    • Also
    • Used
    • Overline
    • Logic
    • Operator
    • Oplus
    • Logical
  • exclusive or
    • Displaystyle
    • Negation
    • Bitwise
    • May
    • Vee
    • Also
    • Used
    • Overline
    • Logic
    • Operator
    • Oplus
    • Logical
  • logical operator
    • Negation
    • Bitwise
    • Operators
    • Overline
    • Equivalence
    • Inclusive
    • Nleftrightarrow
    • Oplus
    • Operation
    • Also
    • Xor
    • One
  • disjunction
    • Exclusive
    • Displaystyle
    • Negation
    • Also
    • Used
    • Bitwise
    • Logic
    • Vee
    • Logical
    • Although
    • Equivalence
    • Overline
  • negation
    • Equivalence
    • Also
    • Overline
    • Logic
    • Vee
    • Nleftrightarrow
    • Operation
    • Operator
    • Displaystyle
    • One
    • Inputs
    • Although
  • two-element field f 2 {\displaystyle \mathbb {f} _{2}}
    • Exclusive
    • Also
    • Nleftrightarrow
    • Oplus
    • Used
    • Logic
    • May
    • Vee
    • Although
    • Following
    • Overline
    • Negation
  • xor gate
    • Operation
    • Used
    • Logical
    • One
    • Addition
    • Also
    • Number
    • Using
    • Displaystyle
    • Two
    • Inputs
    • Following
  • xor swap algorithm
    • Operation
    • Used
    • Logical
    • One
    • Addition
    • Also
    • Number
    • Using
    • Displaystyle
    • Two
    • Inputs
    • Following

Connections between topic areas Semantic bridges

For Exclusive or, one of the stronger structural bridges in this analysis connects Exclusive or with Alternative symbols. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Exclusive or — Alternative symbols · splits 78 ⟂ 26
Exclusive or — Computer science · splits 82 ⟂ 22
Exclusive or — Properties · splits 91 ⟂ 13
Exclusive or — Relation to modern algebra · splits 93 ⟂ 11
Exclusive or — Exclusive or in natural language · splits 94 ⟂ 10
Exclusive or — Overview · splits 95 ⟂ 9
Exclusive or — Equivalences, elimination, and introduction · splits 97 ⟂ 7
Exclusive or — Encodings · splits 101 ⟂ 3

Map overview Semantic statistics

Exclusive or

Nodes104
Edges103
Triples56
Avg. degree1.98
Density0.019231
Components1

Source & methodology

TTTA analyzes the structure around Exclusive or to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Alternative symbols, Computer science & Properties, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Exclusive or · EN edition · Analysis: TopicsToTalkAbout

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