A | B | C | D | E | F | G | H | CH | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
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 |
Logical connectives | ||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
||||||||||||||||||||||
Related concepts | ||||||||||||||||||||||
Applications | ||||||||||||||||||||||
Category | ||||||||||||||||||||||
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.
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).
Notation
And is usually denoted by an infix operator: in mathematics and logic, it is denoted by (Unicode U+2227 ∧ LOGICAL AND),[1] or ; in electronics, ; and in programming languages, &
, &&
, or and
. In Jan Łukasiewicz's prefix notation for logic, the operator is , for Polish koniunkcja.[4]
Definition
Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if (also known as iff) both of its operands are true.[2][1]
The conjunctive identity is true, which is to say that AND-ing an expression with true will never change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result true.
Truth table
The truth table of :[1][2]
F | F | F |
F | T | F |
T | F | F |
T | T | T |
Text je dostupný za podmienok Creative Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších podmienok. Podrobnejšie informácie nájdete na stránke Podmienky použitia.
Antropológia
Aplikované vedy
Bibliometria
Dejiny vedy
Encyklopédie
Filozofia vedy
Forenzné vedy
Humanitné vedy
Knižničná veda
Kryogenika
Kryptológia
Kulturológia
Literárna veda
Medzidisciplinárne oblasti
Metódy kvantitatívnej analýzy
Metavedy
Metodika
Text je dostupný za podmienok Creative
Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších
podmienok.
Podrobnejšie informácie nájdete na stránke Podmienky
použitia.
www.astronomia.sk | www.biologia.sk | www.botanika.sk | www.dejiny.sk | www.economy.sk | www.elektrotechnika.sk | www.estetika.sk | www.farmakologia.sk | www.filozofia.sk | Fyzika | www.futurologia.sk | www.genetika.sk | www.chemia.sk | www.lingvistika.sk | www.politologia.sk | www.psychologia.sk | www.sexuologia.sk | www.sociologia.sk | www.veda.sk I www.zoologia.sk