Question 4 (25 marks): The following transition system describes a process in which people switch on or off the light, and finally leave the room. We use four events, on, off, leave and error, to model the system, and please use the diagra a) please give a trace which contains the event error,and explain the scenerio or meaning of trace. b) Does the process P= on->P[ ]off->satisfies the above transition system,or any trace of the P is not included in the transition system.please explain why it satisfies or does not satisfy. c) We have the following parallel composition SYS which consists of of P and Q with an interface.Please workout the behavior of SYS ,and prove whether it can satisfy the above transition system. P= error > SKIP [ ] off > leave > SKIP Q= on > SKIP III off > leave > SKIP SYS =P[{ error, off, leave }]Q where [ ] denotes the external choice, for interleave and [ I { error, off, leave }] for interface parallel. d)Please work out the FDR scripts for the above transition system