Question $3$

You are asked to design the database structure for an international hotel chain. The following is a list of requirements for the design that you have to model.

The hotel chain owns many hotels.

Each hotel has the following attributes: a unique building ID $($bID$),$ a name that is not necessarily unique, country, state, city, and street address.

A hotel contains a set of rooms, each with a room number. Different hotels can have rooms with the same number, but within a hotel the number is unique.

For each room, we associate with it the maximum number of possible occupants.

A room can be occupied by hotel guests between a given check$-$in and check$-$out date.

Each guest has a guest ID and a name that is not necessarily unique.

The guest who pays for the room is designated as the payer. This person has an attribute, credit card number, associated with him$/$her for the credit card that is used to pay for the stay.

If we model hotels using an entity set, hotel, where each entity $($i$.$e$.,$ hotel$)$ has the attributes given above, then how many possible non$-$overlapping keys $($i$.$e$.,$ sets of attributes that are disjoint$)$ are there for the entity set hotel? Is it possible to uniquely determine a minimal set of attributes to be the key for hotel? $($Note: a set of attributes that form a key is minimal if no smaller subset of these attributes can also form a key.$)$