I'm redrawing these symbols (don't ask why :)) How can I draw them more properly?

(Circle and line segments do not exactly intersect)
My Code:
\documentclass[a4paper]{article}
\usepackage[margin=1.5cm]{geometry}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand{\mycupsymbol}{
\hspace{1.1mm}\tikz[baseline, line width=0.6 pt, line cap=round]{
\draw (1.103,0.08) -- ++(0,0.15);
\draw (0.903,0.08) -- ++(0,0.15);
\draw (1.103,0.08) arc (0:-180:0.1);
}
\hspace{1.1mm}}
\newcommand{\mycup}{\mycupsymbol}
\newcommand{\mycapsymbol}{
\hspace{1.1mm}\tikz[baseline, line width=0.6 pt, line cap=round]{
\draw[line width=0.581] (1.1033,-0.022) -- ++(0,0.15);
\draw[line width=0.581] (0.9033,-0.022) -- ++(0,0.15);
\draw (1.103,0.13) arc (0:180:0.1);
}
\hspace{1.1mm}}
\newcommand{\mycap}{\mycapsymbol}
\begin{document}
$$A_2\mycup \mycap S_2$$
\end{document}

amsmath. (The usage example doesn't even use\[ ... \].) A more appropriate tag might besymbols. – barbara beeton Sep 15 '21 at 19:06