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Logical conjunction
Logical connective AND / From Wikipedia, the free encyclopedia
Not to be confused with Circumflex Agent (^), Capital Lambda (Λ), Turned V (Λ), or Exterior Product (∧).
In logic, mathematics and linguistics, and () is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as
[1] or
or
(prefix) or
or
[2] in which
is the most modern and widely used.
Quick Facts AND, Definition ...
AND | |
---|---|
![]() | |
Definition | |
Truth table | |
Logic gate | ![]() |
Normal forms | |
Disjunctive | |
Conjunctive | |
Zhegalkin polynomial | |
Post's lattices | |
0-preserving | yes |
1-preserving | yes |
Monotone | no |
Affine | no |
Self-dual | no |
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The and of a set of operands is true if and only if all of its operands are true, i.e., is true if and only if
is true and
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).