How do you superimpose two symbols over each other?

Question

I want to superimpose two symbols, e.g. I want to superimpose \vee and \wedge and > and < symbols over each other (not above each other as in stackrel) and Q with a horizontal strike through like bar across it. I am using LyX 2.0.

Answer 1

\rlap and \llap can be used to print a symbol without a width. Similar, the mathtools package provides commands \mathrlap, \mathclap, \mathllap. These commands offer a quick way for overlapping symbols.

Example, overlapping \vee, \wedge and Q like desired in your question:

\documentclass{article}
\usepackage{mathtools}
\begin{document}
$\mathrlap{\vee}\wedge$
\rlap{Q}---
\end{document}

While \rlap produces a zero-width box where the content sticks out to the right, \llap does the same but to the left. \mathclap centers to the current position.

Answer 2

You can define a generic \superimpose macro and then use it for various purposes. Add also the desired math atom class for the built symbol.

Note, however, that \superimpose only makes sense in the context of \mathpalette.

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\newcommand{\superimpose}[2]{{%
  \ooalign{%
    \hfil$\m@th#1@firstoftwo#2$\hfil\cr
    \hfil$\m@th#1@secondoftwo#2$\hfil\cr
  }%
}}
\makeatother
\newcommand{\veewedge}{\mathbin{\mathpalette\superimpose{{\vee}{\wedge}}}}
\newcommand{\lessgreater}{\mathrel{\mathpalette\superimpose{{<}{>}}}}
\newcommand{\strikeQ}{\mathpalette\superimpose{{\textnormal{---}}{Q}}}
\newcommand{\dotineq}{\mathrel{\mathpalette\superimpose{{=}{\cdot}}}}
\begin{document}
$\veewedge_{\veewedge}\lessgreater_{\lessgreater}\strikeQ_{\strikeQ}$
$A\dotineq B$ $\scriptstyle A\dotineq B$
\end{document}

With a different and perhaps more intuitive syntax:

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\newcommand{\superimpose}[3][\mathord]{#1{\mathpalette\superimpose@{{#2}{#3}}}}
\newcommand{\superimpose@}[2]{\superimpose@@{#1}#2}
\newcommand{\superimpose@@}[3]{%
  \ooalign{%
    \hfil$\m@th#1#2$\hfil\cr
    \hfil$\m@th#1#3$\hfil\cr
  }%
}
\makeatother
\newcommand{\veewedge}{\superimpose[\mathbin]{\vee}{\wedge}}
\newcommand{\lessgreater}{\superimpose[\mathrel]{<}{>}}
\newcommand{\strikeQ}{\superimpose{\textnormal{---}}{Q}}
\newcommand{\dotineq}{\superimpose[\mathrel]{=}{\cdot}}
\begin{document}
$\veewedge_{\veewedge}\lessgreater_{\lessgreater}\strikeQ_{\strikeQ}$
$A\dotineq B$ $\scriptstyle A\dotineq B$
\end{document}