4

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?

1 Answer 1

7

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}

enter image description here

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

4
  • 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.
    – egreg
    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.
    – egreg
    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

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