Simple question here. I am trying to enumerate the sigma field generated by the random variable: $X(\omega)=2+1_{\left\{a,b\right\}}(\omega)$ where $\Omega=\left\{a,b,c,d\right\}$.
I think what is confusing me is that I am used to looking for the pre-images under a function in $\mathbb{R}$ or similar. I know the simple discrete space should make this exercise easier, but it just isn't clicking in my head.