You are modeling the requirements for a cruise control system on an automobile. From interviews with the client you have developed the following understanding: The cruise control system is controlled by a master switch and three buttons. Initially, it is turned on by the master switch. The master switch can be turned off at any time. When first turned on, the system enters stand-by mode. When the system is in stand-by mode, the driver of the automobile can press Button 1 to engage the cruise control at the current speed of the automobile. When the cruise control is engaged, if the driver presses the brake or presses Button 1 the system will be disengaged and return to stand-by mode. After returning to stand-by mode, the driver can press Button 2 to engage the cruise control at the speed that it was set at previously. When the cruise control is engaged, the driver can press Button 2 to increase speed by one mile per hour or Button 3 to decrease speed by one mile per hour. Model the system as a finite state machine suitable for discussion with a client. a) What are the states and the transitions for this system? b) Draw the state-transition diagram. c) What is the state-transition table