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Exclusive or

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.

Alternative symbols, Computer science & Properties

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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

Topics to explore

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Overview

Definition

Equivalences, elimination, and introduction

Relation to modern algebra

Exclusive or in natural language

Alternative symbols

Properties

Computer science

Encodings

Advanced semantic analysis

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Map overview Semantic statistics

Exclusive or

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

How this topic connects Entity context

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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 Word statistics

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Important terminology

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

Entity relationships Subject–Predicate–Object triples

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

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