Does anyone know when I would use this symbol ($\supseteqq$) and meaning? Does anyone know what this symbol means? Where would one use it? Someone recently asked me but I do not know what it means. I have seen it with just one line underneath to denote subset. With an equals sign would it mean the trivial subset, meaning $A$ is a subset of $A$?

• $\supseteqq$ means the same as $\supseteq$ (and both should mean the same as $\supset$), the difference is only typographical, in $\supseteqq$, it is harder to overlook the indication of possible equality. – Daniel Fischer Jul 31 '15 at 21:20

It means "is a superset of" as in $\{1,2\}\supseteq\{1\}$.
Saying $A\subset B$ or $A\subseteq B$ means that $A$ is a subset of $B$. Some people use $A\subset B$ meaning that $A\subseteq B$ with $A\neq B$. Another notation for this is $A\subsetneq B$.
Writing $B \supset A$, $B\supseteq A$ and $B\supsetneq A$ is equivalent to the above discussion. There is no difference between $\subseteq$ and $\subseteqq$, etc.