In mathematical expressions, the Exist and does not exist symbols are required. In LaTeX, we will discuss the packages and commands required to write these two symbols in this tutorial.

## Exist symbol in LaTeX

LaTeX provides a default command for printing the Exist symbol in a document, which is `\exists`

. This command must be used in latex math mode.

Symbol | Exist |
---|---|

Type of symbol | Mathematical Operators |

Package | No |

Argument | No |

Latex command | `\exists` |

Example | `\exists` → ∃ |

Below are some examples using this command.

```
\documentclass{article}
\usepackage{amssymb}
\begin{document}
% use amssymb package for \mathbb{}
$$ \verb|\exists|\rightarrow \exists $$
$$ \exists x \in \mathbb{N} $$
$$ {u|\exists v: uv=w} $$
$$ \exists a,b \in \mathbb{R} $$
\end{document}
```

**Output : **

LaTeX also has a package called **semantic**, which provides `\exists`

commands. You can also print the Exist symbol in a LaTeX document using this package. But using the default command and package, there is no difference in the output of the two methods. Take a look.

```
\documentclass{article}
\usepackage{amssymb}
\usepackage{semantic}
\begin{document}
\textbf{Using semantic package}\\
$ \verb|\exists|\rightarrow \exists $\\[4pt]
$ \exists x \in \mathbb{N} $\\[4pt]
$ {u|\exists v: uv=w} $\\[4pt]
$ \exists a,b \in \mathbb{R} $\\
\end{document}
```

**Output : **

## Does not exist symbol in LaTeX

You need a package to print the Does not exist symbol in a LaTeX document, which is **amssymb**. The **amssymb** package provides a `\nexists`

command that allows you to print this symbol into a document.

Symbol | Does not exist |
---|---|

Type of symbol | Mathematical Operators |

Package | amssymb |

Argument | No |

Latex command | `\nexists` |

Example | `\nexists` → ∄ |

```
\documentclass{article}
\usepackage{amssymb}
\begin{document}
$$ \verb|\nexists|\rightarrow \nexists $$
$$ \nexists x.\,P(x) $$
$$ \lim_{x \to 0}x^{-1}=\nexists $$
$$ \lim_{x \to \infty}f\nexists $$
\end{document}
```

**Output : **

There is another alternative way to print the Does not exist symbol, if you use the `\not\exists`

command, the symbol will be printed in a LaTeX document and you do not need to use any package. But you will see some differences in the output of `\nexists`

and `\not\exists`

commands where the `\nexists`

command gives better output. For this I would recommend using `\nexists`

command.

```
\documentclass{article}
\begin{document}
$$ \verb|\not\exists|\rightarrow \not\exists $$
$$ \not\exists x.\,P(x) $$
$$ \lim_{x \to 0}x^{-1}=\not\exists $$
$$ \lim_{x \to \infty}f\not\exists $$
\end{document}
```

**Output : **