# Definition:Open Statement

## Definition

Let $P$ be a statement.

$P$ is an open statement if and only if $P$ contains at least one free occurrence of a variables that appears in it.

## Also known as

An open statement can also be seen referred to as an open sentence.

The word formula can also be seen.

## Examples

### Prime Number

The statement:

$x$ is a prime number

is an open statement, as the variable $x$ appears as a free occurrence.