Question 82
Let $A_1=\varnothing,B_1=\{0\}$. For $n\ge2$, define
$$A_n=\{x+1:x\in B_{n-1}\},\qquad B_n=(A_{n-1}\cup B_{n-1})-(A_{n-1}\cap B_{n-1}).$$
For which $n$ is $B_n=\{0\}$? Here $A-B=\{x\in A:x\notin B\}$.
$$A_n=\{x+1:x\in B_{n-1}\},\qquad B_n=(A_{n-1}\cup B_{n-1})-(A_{n-1}\cap B_{n-1}).$$
For which $n$ is $B_n=\{0\}$? Here $A-B=\{x\in A:x\notin B\}$.