How do I draw the following symbols

The only challenging one is the fourth in the list.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
\langle \cdot,\bullet^{-},\cup,\mathbin{{\bullet}{\breve{\phantom{\imath}}}},1\rangle
\]

\end{document}

Of course you want to make a new command for it.