3. Z Schema (15 marks) We are asked to develop a Z specification for a company that lets its apartments to known customers for fixed time-slots. For that purpose we have developed the following state space schema wherein [APARTMENT, TIMESLOT, PERSON] are Z types representing the set of apartments, timeslots, and persons respectively. TimeShare Co owned P APARTMENT customers P PERSON booked: APARTMENT + (TIMESLOT PERSON) dom booked owned Vap: APARTMENT | ap owned. ran(booked ap) C customers a) Devise a schema that initializes the system. [2 marks] b) Devise a schema for the operation to add a new customer. [4 marks] c) Devise a schema for the operation to acquire a new apartment. [4 marks] d) Devise a schema for the operation to make a booking of a given apartment to a given customer at a given time. [5 marks]