Editing Logical conjunction (section)

{{Short description|Logical connective AND}}
{{Distinguish|Caret{{!}}Circumflex Agent (^)|Lambda{{!}}Capital Lambda (Λ)|Turned v{{!}}Turned V (Λ)|Exterior algebra {{!}}Exterior Product (∧)}}
{{Infobox logical connective
| title        = Logical conjunction
| other titles = AND
| Venn diagram = Venn0001.svg
| wikifunction = Z10174
| definition   = <math>xy</math>
| truth table  = <math>(1000)</math>
| logic gate   = AND_ANSI.svg
| DNF          = <math>xy</math>
| CNF          = <math>xy</math>
| Zhegalkin    = <math>xy</math>
| 0-preserving = yes
| 1-preserving = yes
| monotone     = no
| affine       = no
| self-dual    = no
}}
{{Logical connectives sidebar}}

[[File:Venn 0000 0001.svg|220px|thumb|[[Venn diagram]] of <math>A \wedge B \land C</math>]]

In [[logic]], [[mathematics]] and [[linguistics]], ''and'' (<math>\wedge</math>) is the [[Truth function|truth-functional]] operator of '''conjunction''' or '''logical conjunction'''. The [[logical connective]] of this operator is typically represented as <math>\wedge</math><ref name=":2">{{Cite web|date=2019-08-13|title=2.2: Conjunctions and Disjunctions|url=https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.2%3A_Conjunctions_and_Disjunctions|access-date=2020-09-02|website=Mathematics LibreTexts|language=en}}</ref> or <math>\&</math> or <math>K</math> (prefix) or <math>\times</math> or <math>\cdot</math><ref name=":1">{{Cite web|title=Conjunction, Negation, and Disjunction|url=https://philosophy.lander.edu/logic/conjunct.html|access-date=2020-09-02|website=philosophy.lander.edu}}</ref> in which <math>\wedge</math> is the most modern and widely used.

The ''and'' of a set of operands is true if and only if ''all'' of its operands are true, i.e., <math>A \land B</math> is true if and only if <math>A</math> is true and <math>B</math> is true.

An operand of a conjunction is a '''conjunct'''.<ref name=":21">{{Cite book |last=Beall |first=Jeffrey C. |title=Logic: the basics |date=2010 |publisher=Routledge |isbn=978-0-203-85155-5 |edition=1. publ |location=London |pages=17 |language=en}}</ref>

Beyond logic, the term "conjunction" also refers to similar concepts in other fields:

* In [[natural language]], the [[denotation]] of expressions such as [[English language|English]] "[[Conjunction (grammar)|and]]";
* In [[programming language]]s, the [[Short-circuit evaluation|short-circuit and]] [[Control flow|control structure]];
* In [[set theory]], [[Intersection (set theory)|intersection]].
* In [[Lattice (order)|lattice theory]], logical conjunction ([[Infimum and supremum|greatest lower bound]]).