# What symbol should one use for a set complement?

What symbol should I use for a set complement? It seems that the \complement isn't quite appropriate: it seems taller (perhaps a unary operator to appear before a set?). I guess for now \mathsf{c} works.

• The amsfonts symbol \complement is often used, but there's no general consensus about an "official" symbol. I've seen it denoted in several different ways (personally, I don't like \complement). Commented Apr 17, 2011 at 7:56
• Have a look at “How to look up a math symbol?” for ideas how you can easily find a particular symbol. Commented Apr 17, 2011 at 7:58
• Since the notion of a complement requires a containing set, if that set has a name, say X, then you can simply write $X\setminus A$ where A is the set for which you want the complement.
– TH.
Commented Apr 17, 2011 at 8:06

As the commenters have said, there isn't a strong consensus on this one. Here are a few conventions I know about:

\documentclass{minimal}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand{\eqn}{$\stcomp{(A \cup B)} = \stcomp{A} \cap \stcomp{B}$}

\begin{document}

\newcommand{\stcomp}[1]{{#1}^\complement}  \eqn
\renewcommand{\stcomp}[1]{\overline{#1}}           \eqn
\renewcommand{\stcomp}[1]{{#1'}}           \eqn
\renewcommand{\stcomp}[1]{\widetilde{#1}}           \eqn
\renewcommand{\stcomp}[1]{{#1}^{\sim}}           \eqn
\renewcommand{\stcomp}[1]{{#1}^{\mathsf{c}}}           \eqn
\renewcommand{\stcomp}[1]{X\setminus{#1}}           \eqn

\end{document}


Of all of these I've used ^\complement the most, and the overbar is the one I've seen the most. I have to say I really like your ^\mathsf{c} implementation.

• My textbooks use the minus sign, so that $X - A$ picks out the set of members of X that aren't in A. Is the minus sign commonly used for something else? Commented Feb 18, 2013 at 21:04
• If X is an abelian monoid (i.e., has a subtraction operation) then X-A could be the set of all elements of X which can be expressed as difference of elements of X and A. But I can't say that's a very popular usage. I would be reluctant to use the minus sign when \setminus is available. Commented Feb 20, 2013 at 20:40
• Twofeet, do you mean that your textbooks write $-A$ for the complement of $A$ or simply that they write $X - A$ for the set difference? Either way, I suppose that $\setminus{A}$ (or $\setminus A$) would also be an option for the complement. Commented Dec 5, 2016 at 20:09