Suppose that set \(A\) satisfying \( A \in A\) exists.Then \( \{A\} \subseteq A\).Since \(\{A\}\) is set, there is an element \(a \in \{A\}\) such that \( a \cap \{A\}= \emptyset \). (Axiom of Foundation)\(a \in \{A\}\) implies \(a = A\).Therefore \( A \cap \{A\} = A = \emptyset\)But \(A \in A \cap \{A\}\) since \(A \in A\) and \(A \in \{A\}\), deriving contradiction. To prove a class not exists..