$ S_n = \mathscr P (\{ -n, -n+1, \ldots, n-1, n\}) $ $ R_n = \{r : \Omega - r \in S_n\} $ $ T_n = S_n \cup R_n$
I need to check whether
$T_n$ is an algebra, semi-algebra or sigma algebra.
$T_n \subset T_{n+1}$.
If $T = \bigcup_n T_n$, whether $T$ is algebra, semi-algebra, sigma algebra.
I considered an example for this:
Let $ S_1 = \mathscr P \{-1, 0, 1\} $ $ S_1 = \{\{-1\}, \{0\}, \{1\} ,\{-1,0\}, \{0,1\}, \{-1,1\}, \{-1,0,1\},\{ \varnothing\}\}$
So, for 1) I feel that $T_n = \Omega$, so it can either be any of the algebras.
Please advise.