The relations given below are part of a database schema for a hotel management system. Assume that these relations have been populated with suitable data as appropriate, and the underlined attribute is a primary key.

Hotel (hotelNo, hotelName, city)

Room (roomNo, hotelNo, type, price)

Booking (hotelNo, guestNo, dateFrom, dateTo, roomNo)

Guest (guestNo, guestName, guestAddress)

where Hotel contains hotel details and hotelNo is the primary key;

Room contains room details for each hotel and (roomNo, hotelNo) forms the primary key;

Booking contains details of the bookings and (hotelNo, guestNo, dateFrom) forms the primary key; and

Guest contains guest details and guestNo is the primary key.

Write a relational algebra expression for each of the following data retrieval requirement:

(i) Produce a relation containing the hotel number of those hotels with a room price greater than 50.

(ii) Produce a relation containing the details of all rooms at all hotels.

(iii) Produce a relation containing all hotel names with a room price below 100.

(iv) Produce a relation containing all guests and show the details of any bookings they have beyond 1-Jun-2016.