# Combine universal and existential quantfiers

I want to combine the existential and universal quantifiers so that the left part of the universal quantifier match the right of the existential.

To do so I defined the command:

\newcommand{\quantifs}{\exists\hspace{-3.1pt}\resizebox{7.45pt}{!}{\rotatebox[origin=c]{-20}{$\forall$}}}


Which work well when I type $\quantifs$. However the matching gets all wrong if the sizes change, for example when it is in subscript like in $x_{\quantifs}$.

How can I fix that? Or is there already such symbol defined somewhere?

For a geometric symbol it's better to use geometry. ;-)

\documentclass{article}
\usepackage{amsmath,pict2e}

\newcommand{\quantifs}{\mathpalette\xquantifs\relax}

\makeatletter
\newcommand{\xquantifs}[2]{%
\mspace{1.5mu}%
\sbox0{$\m@th#1\exists$}%
\setlength{\unitlength}{.8\ht0}%
\ifx#1\scriptstyle\linethickness{0.35pt}\fi
\ifx#1\scriptscriptstyle\linethickness{0.3pt}\fi
\begin{picture}(1.55,1.2)
\roundcap\roundjoin
\polyline(0,0.05)(0.75,0.05)(0.75,1.22)(0,1.2)
\polyline(0.05,0.625)(0.75,0.625)
\put(0.75,0.05){\line(5,6){0.8}}
\put(0.75,0.85){\line(11,-5){0.45}}
\end{picture}%
\mspace{1.5mu}
}
\makeatother

\begin{document}

$\exists\quantifs\exists$

$\scriptstyle\exists\quantifs\exists$ $x_{\exists}x_{\quantifs}$

$\scriptscriptstyle\exists\quantifs\exists$

\end{document}


In scriptscript style the reversed E is not as wide as in \exists; this could be fixed, if really needed.

• Thanks a lot!! I was getting a bit irritated with the scale and rotate thing ... That's really helpful! Thanks again!
– wece
May 29, 2015 at 12:41
• @wece The angle at the vertex of the reversed A (\forall) is different in subscript style, so a choice could have been defining different angles for the different styles, but there were also other problems, including different side bearings. So I thought it better to do some measuring and using picture. May 29, 2015 at 12:46
• @wece I made a little fix to get the line thickness even. In second level subscripts the width is not precise, tell me if you need a fix. May 29, 2015 at 12:53
• @egreg Small note: I don't think the counter of the A in the \forall part is actually isosceles. Needs some fine-tuning (or some basic maths). Of course, I may be wrong and this is some optical illusion -- I haven't exactly taken any measurements XD May 29, 2015 at 14:03