---
tag: 0ZGC7ZESYN
kind: concept
name: Proposition
msc: [03B05]
sources:
  - url: https://en.wikipedia.org/wiki/Proposition
    locator: lead section
same_as:
  wikidata: Q108163
  wikipedia: Proposition
---

## Summary

A proposition is a statement that is either true or false.
In classical logic, each proposition has exactly one of the two truth values, true or false.
For example, "$2 + 2 = 4$" is a true proposition, and "$7$ is even" is a false proposition.
A question or a command is not a proposition, because it has no truth value.

## Remarks

Letters such as $p$, $q$ and $r$ usually denote propositions.
An open sentence such as "$x > 3$" is not a proposition until $x$ has a value. It is a [[predicate|0T3DPBG981]].
The connectives [[negation|0XR7A7RSXB]], [[conjunction|0M28ASWG8T]] and [[disjunction|0H5GKDTB01]] make new propositions from given propositions.

## Explanations

### L1 human

A proposition is a sentence that you can mark with "true" or "false".
"It rains in Paris now" is a proposition, because it is true or false at a given time.
"Close the door" is not a proposition, because it is neither true nor false.