Logical conjunction

Logical conjunction

AND
Definition	${\displaystyle xy}$
Truth table	${\displaystyle (1000)}$
Logic gate
Normal forms
Disjunctive	${\displaystyle xy}$
Conjunctive	${\displaystyle xy}$
Zhegalkin polynomial	${\displaystyle xy}$
Post's lattices
0-preserving	yes
1-preserving	yes
Monotone	no
Affine	no
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Logical connectives
AND ${\displaystyle A\land B}$, ${\displaystyle A\cdot B}$, ${\displaystyle AB}$, ${\displaystyle A\&B}$, ${\displaystyle A\&\&B}$ equivalent ${\displaystyle A\equiv B}$, ${\displaystyle A\Leftrightarrow B}$, ${\displaystyle A\leftrightharpoons B}$ implies ${\displaystyle A\Rightarrow B}$, ${\displaystyle A\supset B}$, ${\displaystyle A\rightarrow B}$ NAND ${\displaystyle A{\overline {\land }}B}$, ${\displaystyle A\uparrow B}$, ${\displaystyle A\mid B}$, ${\displaystyle {\overline {A\cdot B}}}$ nonequivalent ${\displaystyle A\not \equiv B}$, ${\displaystyle A\not \Leftrightarrow B}$, ${\displaystyle A\nleftrightarrow B}$ NOR ${\displaystyle A{\overline {\lor }}B}$, ${\displaystyle A\downarrow B}$, ${\displaystyle {\overline {A+B}}}$ NOT ${\displaystyle \neg A}$, ${\displaystyle -A}$, ${\displaystyle {\overline {A}}}$, ${\displaystyle \sim A}$ OR ${\displaystyle A\lor B}$, ${\displaystyle A+B}$, ${\displaystyle A\mid B}$, ${\displaystyle A\parallel B}$ XNOR ${\displaystyle A\ {\text{XNOR}}\ B}$ XOR ${\displaystyle A{\underline {\lor }}B}$, ${\displaystyle A\oplus B}$ converse ${\displaystyle A\Leftarrow B}$, ${\displaystyle A\subset B}$, ${\displaystyle A\leftarrow B}$
Related concepts
Propositional calculus Predicate logic Boolean algebra Truth table Truth function Boolean function Functional completeness
Applications
Digital logic Programming languages Mathematical logic Philosophy of logic
Category
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In logic, mathematics and linguistics, and (${\displaystyle \wedge }$) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as ${\displaystyle \wedge }$^[1] or ${\displaystyle \&}$ or ${\displaystyle K}$ (prefix) or ${\displaystyle \times }$ or ${\displaystyle \cdot }$^[2] in which ${\displaystyle \wedge }$ 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., ${\displaystyle A\land B}$ is true if and only if ${\displaystyle A}$ is true and ${\displaystyle B}$ is true.

An operand of a conjunction is a conjunct.^[3]

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

• In natural language, the denotation of expressions such as English "and";
• In programming languages, the short-circuit and control structure;
• In set theory, intersection.
• In lattice theory, logical conjunction (greatest lower bound).