Hi

Let be a finite set. Show that the set of all subsets of , , is also finite and that it is a -algebra.

Solution (?)

Since is finite, such that . From set theory we know that the number of subsets of a finite set of cardinality is . Therefore,

, since . Hence, is finite.

and is in . Since contains all subsets of it must also contain all necessary unions, intersections and complements to make a -algebra.

Comments/improvements?

Thanks!