Forming a sigma field from a countable infinite set

[johnG2011]

The professor did this problem in class but I need help with understanding it a little more.

For any countably infinite set, the collection of its finite subsets and their complements form a field F.

Prove that this conjecture.

 

[mathman]

A field is defined as a collection which includes all finite unions and intersections as well as complements. A finite union or intersection of finite sets is finite. To handle complements, use the fact that the complement of unions is the intersection of complements, etc.