Given the sample space S, an event E, and the sigma algebra on S. Mark all the correct statements about the sigma algebra:

1 if E is an element of the sigma algebra, its complement is not necessary in the sigma algebra

2 the sigma algebra is closed under complements

3 S ; i.e. the sample space does not belong to the sigma algebra.

4 if every finite and countable collection of events Ei is contained in the sigma algebra, so its union;

i.e. EiE1UE2U...UEn

5 , i.e. the empty set belongs to the sigma algebra