How to write an empty(or null) set symbol(∅) in LaTeX?

An empty set, also known as a null set, is a unique set that contains no elements. Mathematically, it is represented by either the phi symbol (∅) or curly brackets {}.

Empty set symbol

In LaTeX, the most commonly used command to represent the empty set is \emptyset. It is widely accepted and does not require any additional packages.

\(p=\left \{ x:x^{2}=4,x\:is\:odd\right \} \)
\( \therefore p=\emptyset \)

Output :

In above code, the \: command is used to add extra space between words in the equation, improving readability.

Using the \O Command

Alternatively, the \O command can be used for the same symbol. While the meaning remains identical, the structure of the symbol is slightly different.

\( p=\left \{ x:x^{2}=9,x\:is\:even\right \} \)
\( \therefore p=\O \)

Output :

Using the \varnothing Command

The \varnothing command is another way to represent the empty set symbol (∅) in LaTeX. However, this command requires the amssymb package to function properly.

\documentclass{article}
\usepackage{amssymb}
\begin{document}
  \[ p=\left \{ x:x\:is\:odd\right \]
  \[ q=\left \{ x:x\:is\:even\right \] 
  \[ \therefore p\cap q=\varnothing \]
\end{document}

Output :

For standard usage in scientific and mathematical documents, \emptyset is the best choice

Using curly brackets symbol

Although curly brackets {} are available on your keyboard, in LaTeX, it is best to use \left\{ ... \right\}. This ensures that the brackets automatically adjust their size based on the enclosed content.