Set theory bracket notation, what is excluded $X=\{\emptyset,\{\emptyset\},\{\{\emptyset\}\}\}$ and $Y=X\setminus\{\{\emptyset\}\}$ If $X=\{\emptyset,\{\emptyset\},\{\{\emptyset\}\}\}$ and $Y=X\setminus\{\{\emptyset\}\}$ 
then what element is excluded from $X$? Is it $\{\{\emptyset\}\}$, or $\{\emptyset\}$?
In a similar vein, if $Z=\{a, b, c\}$, does it make sense to say $Z\setminus a$?
Thanks

$$X=\{\emptyset,\{\emptyset\},\{\{\emptyset\}\}\}$$
and $$ Y=X\setminus\{\{\emptyset\}\}=   \{\emptyset,\{\{\emptyset\}\}\}    $$ because $\{\emptyset\}$ is removed from your $X$.
For your next question regarding $$ Z=\{a, b, c\}$$ $Z\setminus a$ does not make sense unless $a$ is a set.
