Axiom of Regularity and Self-Containment

Question

I understand that the axiom of Regularity excludes $A=\{A\}$ but what about $A=\{A, \emptyset \}$?

Answer 1

If $A = \{A,\emptyset\}$ then $A \in A$ which is impossible with Regularity.

Answer 2

By pairing+comprehension there exists a set $B=\{A,A\}=\{A\}$ and then $B\cap A=\{A\}\cap\{A, \emptyset\}=\{A\}\ne\emptyset$, and since $A$ is the only member of $B$, $B$ violates the axiom of regularity.