Set Minus in LaTeX (\setminus)

Where it is used

Set difference operator: A \setminus B is the set of elements of A not in B.

Use \setminus for set difference, A \setminus B, and for removal, \mathbb{R} \setminus \{0\}. It is a binary operator with proper spacing, while \backslash looks the same but is an ordinary symbol used for quotients like G \backslash X (left cosets). A smaller variant \smallsetminus suits some fonts better. Some authors write A - B instead, but \setminus avoids confusion with subtraction. Combined with \complement: A \setminus B = A \cap B^\complement. In fractions like G \backslash X / H for double cosets, keep \backslash for the quotient instead.

Also listed under: Set Theory

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\usepackage{amssymb}
\begin{document}
Set Minus: $\setminus$

\[ A \setminus B = A \cap B^{\complement} \]
\end{document}

Related symbols

• Wreath Product\wr
• Double Dagger\ddagger
• Dagger\dagger
• Amalgamation\amalg
• Intersection\cap
• Union\cup

Frequently asked questions

How do I write Set Minus in LaTeX?

Type \setminus in math mode, for example $A \setminus B = A \cap B^{\complement}$. It works in plain LaTeX without loading any package.

Which package do I need for \setminus?

None. \setminus is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \setminus in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\setminus$ in running text. If you only need the glyph in text, paste the Unicode character ∖ instead (with XeLaTeX or LuaLaTeX and a font that has it).