Is the empty set the only possible set for $A$ such that $A=\{x|x\not\in A\}$? Is the empty set the only possible set for $A$ such that $A=\{x|x\not\in A\}$?

The complement of $A$, $A^c$ is such that $$A^c = \{x\mid x\notin A\}$$ A set cannot also be its own complement, and we have $A\neq A^c \implies A\neq \{x\mid x \notin A\}$
