---
tag: 0M28ASWG8T
kind: definition
name: Conjunction
msc: [03B05]
defines: 025YZN3VJW
uses: [0ZGC7ZESYN]
sources:
  - url: https://en.wikipedia.org/wiki/Logical_conjunction
    locator: lead section
---

## Definition

Let $p$ and $q$ be [[propositions|0ZGC7ZESYN]].
The conjunction of $p$ and $q$ is the proposition $p \land q$, read "$p$ and $q$".
The proposition $p \land q$ is true when $p$ is true and $q$ is true. In all other cases, $p \land q$ is false.

| $p$ | $q$ | $p \land q$ |
|---|---|---|
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |

## Remarks

Conjunction is commutative and associative: $p \land q$ has the same truth value as $q \land p$.
The [[intersection|0HBRW4E6G1]] of two sets uses conjunction: $x \in A \cap B$ means $x \in A \land x \in B$.

## Explanations

### L1 human

The sentence "$6$ is even and $6$ is divisible by $3$" is a conjunction.
It is true, because both parts are true.
If one part is false, the whole sentence is false.