Which of the following is false?

I. Domain Name System is a distributed database implemented in a hierarchy of many name servers.

II$.$ Even though DNS is a core Internet function, it is implemented as an application$-$layer protocol.

III. DNS has the following order of name server hierarchy:

Root servers

Authoritative servers

Top Level Domain $($TLD$)$ servers

IV$.$ Domain Name System has $13$ logical root name servers throughout the world. Each server is replicated many times.