Mathematical symbol for disjoint set union

Another possibility to go around the problem that there is no such symbol in amssymb is to use the dot-accent: \dot{\bigcup} or also \dot\bigcup. This works for all symbols, and might very well be the reason that there are no dotted symbols in amssymb.

To let TeX treat such a new construct as an operator in terms of spacing though, you need to use \mathop and \mathbin, that's to say \mathop{\dot{\bigcup}} and \mathbin{\dot{\cup}}.

Edit I thought amssymb provides \cupdot which does what you want... but it doesn't.

\usepackage{MnSymbol} provides \cupdot and \bigcupdot but is incompatible with amssymb which is unfortunate.

Sometimes disjoint union is depicted using \sqcup which has the advantage of being in amssymb

Disjoint union is also sometimes written using \coprod, since it is in fact the coproduct in the category of sets.