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[[File:Logical_connectives_Hasse_diagram.svg|thumb|Logical_connectives_Hasse_diagram]] [[file:Red_Square.svg|right|thumb|Red_Square]] [[file:Blank_Square.svg|right|thumb|Blank_Square]] [[file:Venn01.svg|thumb|Venn01]] [[file:Venn10.svg|thumb|Venn10]] [[file:Venn0101.svg|thumb|Venn0101]] [[file:Venn0011.svg|thumb|Venn0011]] {{Short description|Symbol or word used to connect two or more sentences in a logical manner}}
{{other uses|Logical connective (disambiguation)}}

A '''logical connective''' (also called a '''logical operator''', '''sentential connective''', or '''propositional connective''') is a symbol or word used to connect two or more [[proposition]]s in a [[logical formula]] to form a [[compound proposition]]. Logical connectives are fundamental to the field of [[propositional logic]] and are used to build complex logical expressions from simpler ones.

== Types of Logical Connectives ==
Logical connectives can be classified into several types based on their function:

* '''Conjunction''' (AND, ∧): The conjunction of two propositions is true if and only if both propositions are true.
* '''Disjunction''' (OR, ∨): The disjunction of two propositions is true if at least one of the propositions is true.
* '''Negation''' (NOT, ¬): The negation of a proposition is true if the proposition is false.
* '''Implication''' (IF...THEN, →): The implication is true if the first proposition implies the second proposition.
* '''Biconditional''' (IF AND ONLY IF, ↔): The biconditional is true if both propositions are either true or false.

== Truth Tables ==
Logical connectives are often defined using [[truth table]]s, which show the truth value of a compound proposition for every possible combination of truth values of its components.

=== Conjunction (AND) ===
{| class="wikitable"
|-
! P !! Q !! P ∧ Q
|-
| T || T || T
|-
| T || F || F
|-
| F || T || F
|-
| F || F || F
|}

=== Disjunction (OR) ===
{| class="wikitable"
|-
! P !! Q !! P ∨ Q
|-
| T || T || T
|-
| T || F || T
|-
| F || T || T
|-
| F || F || F
|}

=== Negation (NOT) ===
{| class="wikitable"
|-
! P !! ¬P
|-
| T || F
|-
| F || T
|}

=== Implication (IF...THEN) ===
{| class="wikitable"
|-
! P !! Q !! P → Q
|-
| T || T || T
|-
| T || F || F
|-
| F || T || T
|-
| F || F || T
|}

=== Biconditional (IF AND ONLY IF) ===
{| class="wikitable"
|-
! P !! Q !! P ↔ Q
|-
| T || T || T
|-
| T || F || F
|-
| F || T || F
|-
| F || F || T
|}

== Applications ==
Logical connectives are used in various fields such as [[mathematics]], [[computer science]], [[philosophy]], and [[linguistics]]. In [[computer programming]], logical operators are used to control the flow of execution and to perform logical operations on data.

== Related Pages ==
* [[Propositional logic]]
* [[Truth table]]
* [[Boolean algebra]]
* [[Predicate logic]]
* [[Logical equivalence]]
* [[Logical consequence]]

== See Also ==
* [[Boolean function]]
* [[Logical constant]]
* [[Tautology (logic)]]
* [[Contradiction]]

[[Category:Logic]]
[[Category:Mathematical logic]]
[[Category:Philosophical logic]]
[[Category:Computer science]]

{{Logic-stub}}

Logical connective - Revision history

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