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When I use

$(LM)^\ast = (LM)^(0) \ucup (LM)^(1)\ucup (LM)^(2) $

I receive an error:

--this is a undefined control sequence

I need to use (LM)^*= (LM)^0 \ucap (LM)^1 \ucap..

and so on. How should I make it in LaTeX?

2

There is no symbol \ucup or \ucap; use \cup or \cap. Also, for superscripts (or subscripts that contain more than one token, brace them:

enter image description here

\documentclass{article}
\begin{document}
$(LM)^\ast = (LM)^{0} \cup (LM)^{1} \cup (LM)^{2}$
\end{document}

You can also find many other symbols in the Comprehensive LaTeX Symbol List.

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