Logical conjunction

In logic, mathematics and linguistics, And (${\displaystyle \wedge }$) 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. The logical connective that represents this operator is typically written as ${\displaystyle \wedge }$ or ⋅ .[1][2]

Quick facts: AND, Definition, Truth table, Logic gate, Nor... ▼

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
v t e

${\displaystyle A\land B}$ is true if and only if ${\displaystyle A}$ is true and ${\displaystyle B}$ is true, otherwise it is false.

An operand of a conjunction is a conjunct.

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).
• In predicate logic, universal quantification.