the answer, as you said, is no. suppose is an infinite set. then and thus is not a sigma algebra.

let then because each is a finite set. but because neither nor the complement of in is finite. so is not a sigma algebra.2. Omega = R (real line)

F = {A subset R : A is finite or A' is finite}. Is F a sigma algebra?

This is where my suspicion about my interpretation grew. I mean, there wouldn't be a need to mention A' if it isn't even in F right? So, the question is, what exactly is contained in F in both cases?

now try thisexercise: let be any set and is a sigma algebra?