Write with z notation the following : The system allows a schedule of public events to be created, updated and used. The system records the sequence of activities forming the specified event. Each activity is characterized by a start time and location. A schedule can represent parallel sequences of activities that also have common slots $($opening$,$ breaks$).$ The invariant of the system is that there cannot be activities at the same time, place, and responsible in a schedule with parallel sequences of activities other than shared slots.

A$)$ Model the basic state of an event system and its initialization under two parallel sequences of activities with common discovery.

B$)$ Describe a robust operation for:

a$)$ Entry of an activity into one of the two sequences of activities, part of an event.

b$)$ Correction of time and place of activity in an existing schedule.

c$)$ A reference to the sequence of all activities in a certain time interval.W