Translate a measure theory problem in German to English

Question

Für jede natürliche Zahl $n \in \mathbb{N}$ sei $A_n$ die von der Mengenfamilie $\{\{1\}, \{2\}, \dots , \{n\}\}$ erzeugte sigma-algebra auf $\mathbb{N}$. Zeigen Sie, daß $A_n$ neben $B = \emptyset$ und $B = \mathbb{N}$ aus allen Mengen $A \subset \mathbb{N}$ besteht, welche entweder $A \subset \{1, \dots, n\}$ oder $m \in B$ für alle $m \geq n +1$ erfüllen

This is what I have come up with:

For every natural number $n \in \mathbb{N}$, let $A_n$ be the family of sets $\{\{1\}, \{2\}, \dots , \{n\}\}$ which generates a sigma-algebra on $\mathbb{N}$. Show that $A_n$ [...]

Answer 1

For every natural number $n \in \mathbb N$, let $A_n$ be the $\sigma$-algebra on $\Bbb N$ generated by $\{ \{1\},\cdots,\{n\} \}$. Show that $A_n$ consists, besides $B = \varnothing$ and $B = \mathbb N$, of all subsets $B$ which satisfy $B \subseteq \{1,\cdots,n\}$ or $m \in B$ for all $m \ge n+1$.

Note 1 : There were obvious typos in the question, I also corrected them.

Note 2 : The cases $B = \varnothing$ and $B = \mathbb N$ do not need to be excluded... this exercise looks like it's been written by a very strange mathematician.

Hope that helps,