---
tag: QS0XVAN9BG
kind: concept
name: Logical connective
msc: [03B05]
sources:
  - url: https://en.wikipedia.org/wiki/Logical_connective
same_as:
  wikidata: Q211790
  wikipedia: Logical connective
---

## Summary

A logical connective is a symbol that builds a new formula from one or more given formulas.
The usual connectives are [[negation|029JBBF693]] $\neg$, [[conjunction|025YZN3VJW]] $\land$, [[disjunction|0F72FK8EKB]] $\lor$, [[implication|0NMG7W7Q11]] $\to$ and the [[biconditional|0S6GMNJ62Y]] $\leftrightarrow$.
In classical logic, each connective is given by a truth function, which a [[truth table|05RSK4Q657]] displays.
Connectives are the glue of [[propositional logic|09K9MWD2QQ]] and of [[predicate logic|086QKPF0A6]].

## Explanations

### L1 human

Connectives are the words "not", "and", "or", "if ... then" and "if and only if", written as symbols.
They join simple statements into compound ones.
For example, from $p$: "it rains" and $q$: "it is cold", the connective $\land$ builds $p \land q$: "it rains and it is cold".
In classical logic, the truth of the compound statement depends only on the truth of its parts.