Proving finite intersection closure in sigma algebras

[Kuma]

If A is a sigma algebra on a set S.

if Ai E A. i = 1,...,n
prove that the intersection of all Ai E A.

now isn't the intersection just the empty set in this case? Which is already proved as the empty set is always contained in A?

 

[mathman]

Why would the intersection of the Ai be empty?