How to get the width for a math symbol to align the rows of a table?

Question

I try to align the letters b,d,t exactly vertically stacked. But the \neg symbol has unkown width. What is it and how to find it out in general? Numerous spacings exist, but whats the exact one?

\documentclass{article}
\usepackage{amsmath, booktabs}

\begin{document}
\begin{tabular}{@{}ll@{}}
\toprule
combination         & example \\ \midrule
$(b,\ \ \ d,\ \ \ t)$           &         \\
$(b,\ \ \ d,\neg t)$      &         \\
$(b,\neg d,\ \ t)$      & double auction \\
$(b,\neg d,\neg t)$ &         \\ \bottomrule
\end{tabular}
\end{document}

Answer 1

\hphantom{\neg} will insert a horizontal space exactly the same as \neg

\documentclass{article}
\usepackage{amsmath, booktabs}

\begin{document}
\begin{tabular}{@{}ll@{}}
\toprule
combination         & example \\ \midrule
$(b,\hphantom{\neg} d,\hphantom{\neg} t)$           &         \\
$(b,\hphantom{\neg} d,\neg t)$      &         \\
$(b,\neg d,\hphantom{\neg} t)$      & double auction \\
$(b,\neg d,\neg t)$ &         \\ \bottomrule
\end{tabular}
\end{document}

Answer 2

This makes all components the same width, specified here as 2.1ex, plus an added inter-column gap of \,\,.

This allows some flexibility if the array content changes and allows for the presence of \neg in the first column.

\documentclass{article}
\usepackage{amsmath, booktabs}
\newcommand\cw{2.1ex}
\def\z(#1,#2,#3){%
  (\makebox[\cw][r]{$#1$},\,\,\makebox[\cw][r]{$#2$},\,\,\makebox[\cw][r]{$#3$})}
\begin{document}
\begin{tabular}{@{}ll@{}}
\toprule
combination         & example \\ \midrule
$\z(b,d,t)$           &         \\
$\z(b,d,\neg t)$      &         \\
$\z(b,\neg d,t)$      & double auction \\
$\z(b,\neg d,\neg t)$ &         \\ \bottomrule
\end{tabular}
\end{document}

But if you wanted the output tailored to this particular set of arrays, then

\documentclass{article}
\usepackage{amsmath, booktabs}
\setbox0=\hbox{$b$}
\edef\cwA{\the\wd0}
\setbox0=\hbox{$\neg d$}
\edef\cwB{\the\wd0}
\setbox0=\hbox{$\neg t$}
\edef\cwC{\the\wd0}
\def\z(#1,#2,#3){%
  (\makebox[\cwA][r]{$#1$},\,\,\makebox[\cwB][r]{$#2$},\,\,\makebox[\cwC][r]{$#3$})}
\begin{document}
\begin{tabular}{@{}ll@{}}
\toprule
combination         & example \\ \midrule
$\z(b,d,t)$           &         \\
$\z(b,d,\neg t)$      &         \\
$\z(b,\neg d,t)$      & double auction \\
$\z(b,\neg d,\neg t)$ &         \\ \bottomrule
\end{tabular}
\end{document}

Answer 3

Another way uses the \eqparbox package, which defines a system of tags for the standard box commands: all boxes sharing the same tag have as width of the natural width of the widest box in the series.

\documentclass{article}
\usepackage{amsmath, booktabs}
\usepackage{eqparbox}
\newcommand{\eqmathbox}[2][T]{\eqmakebox[#1][r]{$#2$}}

\begin{document}

\begin{tabular}{@{}ll@{}}

\toprule
combination & example \\ \midrule
$(b, \eqmathbox[D]{d},\eqmathbox{ t})$ & \\
$(b,\eqmathbox[D]{d}, \eqmathbox{t})$ & \\
$(b,\eqmathbox[D]{\neg d}, \eqmathbox{t})$ & double auction \\
$(b,\eqmathbox[D]{\neg d},\eqmathbox{\neg t})$ & \\ \bottomrule
\end{tabular}

\end{document}