Say we have 3 sets $A,B$ and $C$ and
$A\cap C =\varnothing$
$B\cap C = \varnothing$
$S\setminus A = B$
where $S$ is the sample space.
The question is whether $\{A,B\}$ is an event space or not. I am not able to figure out how to solve this, do i make a venn diagram or something? How would that look like cause I don't get how $S\setminus A = B$ part will work in that.
Formally an event space is a $\sigma$-algebra $\mathcal A$ with $\mathcal A\subseteq\wp(S)$ where $S$ denotes the sample space.
That means that also $\varnothing$ and $S$ must be elements of $\mathcal A$.
This is not guaranteed by the data.
Only in the special cases $\langle A,B\rangle=\langle\varnothing, S\rangle$ and $\langle A,B\rangle=\langle S,\varnothing\rangle$ the set $\{A,B\}$ is a $\sigma$-algebra.