Custom Symbol Creation | Union and Intersection

Question

I am a beginner in LaTeX and was wondering if someone could help me with the following problem.

I will be soon embarking on a re-formatting journey of a certain article and believe that I have most of the solutions covered. However, there is one which is beyond my current level of knowledge. The author used a certain custom symbol which I can't recreate. Please find the below screenshot:

I have tried joining \cup and \cap together and adjusting their position but the result was far from satisfying. Upon searching for a solution, I have stumbled upon this post:

How to add a custom symbol to LaTeX?

And was impressed what can be achieved with the TikZ and PGF packages. However, when I opened the Tikz and PGF Manual, I understood that I wouldn't get away quickly with a solution.

I wanted to ask for help in creating the above-mentioned symbol using \usepackage{tikz}, unless there is a better solution for getting the same result?

Answer 1

You could use the picture environment with the enhancements of the pict2e package.

\documentclass{article}
\usepackage{pict2e}
\newcommand*{\cupcap}{%
    \mathrel{%
        \begin{picture}(8,8)
            \roundcap
            \put(0,2){\line(0,1){5}}
            \put(2,2){\arc[180,360]{2}}
            \put(4,2){\line(0,1){3}}
            \put(6,5){\arc[180,0]{2}}
            \put(8,0){\line(0,1){5}}
        \end{picture}%
    }%
}
\begin{document}
\( X \cupcap Y \)
\end{document}

Answer 2

Welcome to StackExchange!

Here is the symbol and its mirror. I've commented the code so that you can tailor it to your liking. I looked for a Unicode symbol for this but came up dry. Odd -- I could have sworn I've seen this in print.

\documentclass[]{standalone}

\usepackage{tikz}

\def\symbol{%
    \mathrel{%
    \begin{tikzpicture}[baseline]% Makes sure that the symbol is on the baseline
        \def\r{0.18em}% radius of the arc
        \def\h{0.475em}% determines height of the symbol
        \draw[line width=0.06em](0,\r+\h) -- %% Adjust line width to suit
            (0,\r)
            arc (180:360:\r) -- %% the lower arc overshoots the baseline as it should
            (2*\r,\h)
            arc (180:0:\r) -- 
            (4*\r,0);%
    \end{tikzpicture}%
    }%
}

\def\ssymbol{% reflected
    \mathrel{%
    \begin{tikzpicture}[baseline]% Makes sure that the symbol sits on the baseline
        \def\r{0.18em}% radius of the arc
        \def\h{0.475em}% determines height of the symbol
        \draw[line width=0.06em](0,0) -- %% Adjust line width to suit
            (0,\h)
            arc (180:0:\r) --
            (2*\r,\r)
            arc (180:360:\r) -- %% the lower arc overshoots the baseline as it should
            (4*\r,\h+\r);%
    \end{tikzpicture}%
    }%
}

\begin{document}

$x^2\symbol Z$ or $A\ssymbol B$

\end{document}

Answer 3

A solution with TikZ:

\documentclass{article}
\usepackage{tikz}
\newcommand*{\cupcap}{\mathrel{%
\def\hs{0.62em}%heigth symbol
\def\ws{0.9*\hs}%width symbol
\def\lw{0.12*\hs}%line width
\tikz[baseline=0pt]{
    \draw[rounded corners=0.15*\hs,%<-roundness of the symbol
           line width=\lw]%
     (0,0) -- ++(0,\hs+0.5*\lw) -- ++(-0.5*\ws,0) -- ++(0,-\hs) --
       ++(-0.5*\ws,0) -- +(0,\hs+0.5*\lw);%
        }%
    }%
}
\begin{document}
\( \mathsf{X} \cupcap \mathsf{Y} \)
\end{document}

Answer 4

If that fit well with the default \cup and \cap is another story, but simply turning the "S" of some fonts:

\documentclass{article}
\usepackage{graphicx}
\newcommand\ui{{\:\mbox{{\font\fetamont=ffml10
\fetamont\resizebox{.75em}{!}{\rotatebox[origin=c]{90}{\char115}}}}}\:}
\begin{document}
$(X \cup  Y \cap Z \ui W)$\par
$(X \ui Y)$\par
\end{document}