Let $(\Omega, \mathscr F, \mathbb P)$ be a probability space.

Let events $A_{1,n}, A_{2,n}, A_{3,n}, ...$ be n-wise independent for $n \in \mathbb N$

Define $I_m := \liminf_n A_{m,n}, S_m := \limsup_n A_{m,n}$.

1. Are $I_1, I_2, ...$ independent?

2. Are $S_1, S_2, ...$ independent?